A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

pooja195

  • one year ago

@mathmate

  • This Question is Closed
  1. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @mathmate

  2. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Nnesha its not spam ;)

  3. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Nnesha its not spam ;)

  4. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes!

  5. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What's your question?

  6. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    O_o question? XD 2+2=?

  7. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Not allowed to give direct answers. Check the drawing: |dw:1433043776037:dw|

  8. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    4 LOL

  9. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @mathmate ;-;

  10. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That means: 1. i dont like this and 2. i dont understand this OR 3. i dont want to do this Which one/ones?

  11. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    3 +_+

  12. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    gimme a minute!

  13. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Calculate \(\large \frac{1}{2}+\frac{2}{3}\). Show work.

  14. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    7/6

  15. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Calculate 12+23. \(\huge \color{red}{Show work.}\)

  16. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Why are we doing this? .-.

  17. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Because it is the same way you do this as with rational fractions. This is a pretest!

  18. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[12+23=35\]

  19. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    idk how to show work for that .-.

  20. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2+1=3 3+2=5

  21. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, that's how it works: Calculate \(\large \frac{1}{2}+\frac{2}{3}\), show work.

  22. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large \frac{1}{2}+\frac{2}{3}=\frac{1*3}{2*3}+\frac{2*2}{3*2}\)

  23. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you know why we multiply the first fraction by three, and the second by two?

  24. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    to get a common denominator

  25. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Exactly!

  26. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just a review of terms: 1/2 = 2/4 because they are __________________

  27. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    equivalent

  28. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    exactly "equivalent fractions"! That's a good start! You know your stuff.

  29. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

  30. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The idea of adding and subtracting rational fraction is exactly the same!

  31. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We multiply top and bottom of each term by a factor so that the denominator becomes the common denominator.

  32. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Since each term remains an equivalent fraction, the answer will not change, BUT...

  33. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we now only have to add the numerators of the equivalent fractions, just like the numerical example.

  34. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large \frac{1}{2}+\frac{2}{3}=\frac{1*3}{2*3}+\frac{2*2}{3*2}=\frac{3}{6}+\frac{4}{6}=\frac{7}{6}\)

  35. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry it took a while!

  36. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this looks easy :)

  37. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The next one will be equally easy! gimme a minute.

  38. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Calculate \(\large \frac{1}{x}+\frac{2}{x^2}\) show work!

  39. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~\frac{ 1*x }{ x*x }+\frac{ 2 }{ x^2}=\frac{ 1x+2 }{ x^2 }\]

  40. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent! Just remember that 1x is usually written as x, except when showing work.

  41. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now: Calculate \(\large \frac{2}{(x-1)}-\frac{1}{(x-1)^2}\) show work!

  42. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{ 2*(x-1) }{ (x-1)*(x-1) }-\frac{ 1 }{ (x-1)^2 }=\frac{ 1(x-1) }{ (x-1) }=1\]

  43. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The denominator is still meant to be (x-1)^2 ? You need to do the math on the numerators. Give it another shot!

  44. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    T_T not allowed!

  45. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ;-;

  46. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i dont get it

  47. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good! I'll explain!

  48. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large \frac{ 2*(x-1) }{ (x-1)*(x-1) }-\frac{ 1 }{ (x-1)^2 }\) is perfect!

  49. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    At this point, both denominators are identical, so we can do the math just on the numerators \(\large \frac{ 2*(x-1) -1 }{ (x-1)^2 }\)

  50. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    following so far?

  51. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  52. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now can you do the math (on the numerator) and finish?

  53. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{ x(x-1) }{ (x-1)^2 }\]

  54. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You need to distribute the first term, and add like terms, 2*(x-1)-1 = 2x-2 -1 =2x-3

  55. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    following?

  56. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes

  57. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So the final answer is....

  58. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge\frac{ x(x-1) }{ 2x-3 }\]

  59. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    >_<

  60. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wrong spot...

  61. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{ 2x-3 }{ (x-1)^2 }\]

  62. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Whew! Yes, excellent!

  63. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    One thing we did without saying it is...nothing. We did "nothing" to factorize the numerator, because it was "obvious" there are no factors.

  64. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    In general, after the arithmetic on the numerator, we need to factor the numerator, can you tell me why?

  65. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :/ so its easier to multiply or is it to break down the numbers? :/

  66. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So that we can cancel (with condition) IF there are common factors between the numerator and denominator, just like what we did before in the simplification. Does that make sense?

  67. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  68. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Are there any points to clarify, or are we good?

  69. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We're good.

  70. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, now, try this: Calculate \(\large \frac{3}{x}-\frac{2}{x-1}\) show work!

  71. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ummm O_O

  72. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Look at the denominators.

  73. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    there are no common factors! So you just "cross multiply", which is a short cut when there are no common factors. like \(\large \frac{1}{2}+\frac{3}{5}= \frac{1*5}{2*5}+\frac{2*3}{x*5}=\frac{1*5+2*3}{2*5}=\frac{11}{10}\)

  74. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    * 2*5 in denominator

  75. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    O_o

  76. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i thought u can only do that if there is an equal sighn :/

  77. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It's not a real cross multiplication, but it works in a similar way.

  78. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The pattern helps when there are no common factors. You can use that in the new problem.

  79. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Calculate \(\large \frac{3}{x}-\frac{2}{x-1}\), show work! Remember that when there is no common factors in the denominators, the common denominator is just the product, namely x(x-1)

  80. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :?

  81. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large \frac{3}{x}-\frac{2}{x-1}=\frac{3(x-1)}{x(x-1)}-\frac{2x}{(x-1)x}=\frac{3(x-1)-2x}{x(x-1)}\)

  82. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm ok makes a bit more sense

  83. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good! you can finish it?

  84. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{ x-1 }{ x(x-1) }\]

  85. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    brb

  86. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    IF it was x(x-1)/(x-1), you would have simplified it to x, x\(\ne\)1. But 3(x−1)−2x=3x-3 -2x (distribute 3(x-1) to 3x-3 first, then add -2x) =x-3

  87. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    With x-3 as numerator, what would the answer be then?

  88. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    >_< idk :(

  89. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the common denominator does not change, so still x(x-1) Answer would then be: \(\huge \frac{ x-3 }{ x(x-1) }\) nothing to further simplify!

  90. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Here's one for you to think about when I'm off for a few minutes. Calculate \(\large \frac{2}{(x+1)}+\frac{1}{(x-1)}\) , show work! Do remember to work out the math in the numerator, and the common denominator (product of x+1 and x-1) does not change.

  91. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @pooja195

  92. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{ (x-1)*2 }{ (x-1)*(x+1) }+\frac{ (x+1)*1 }{ (x+1)*x-1) }=\frac{ 3(x+1)(x-1) }{ (x-1)(x+1) } \]

  93. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The first part is very good!

  94. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Recall that since the denominator is the same, and does not change, we need to ADD the numerators (and not multiply).

  95. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So it would read: \(\LARGE \frac{ (x-1)*2 + (x+1)*1}{ (x-1)(x+1) }\) \(=\LARGE \frac{ 2X-2 + X+1}{ (x-1)(x+1) }\) \(=\LARGE \frac{ 3X-1 }{ (x-1)(x+1) }\), OR \(=\LARGE \frac{ 3X-1 }{ x^2-1 }\)

  96. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    O_O

  97. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Your steps are correct. It's just the last step of expanding and adding that there was a correction to make. Are you ok with the correction, or confused?

  98. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x_x

  99. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, if it's the part of expansion perhaps you could use some help. (x-1)*2 + (x+1)*1 is the same as 2(x-1) + (x+1) .... a coefficient of 1 is understood. Then we distribute, basically a half FOIL 2*x + 2*(-1) + x+1 ..... parentheses after a plus sign can be removed without change that makes 2x -2 +x +1 Now add like terms 2x+x -2+1 =3x-1 this is the numerator, since the denominator does not change, we have as the answer: =\(\Large \frac{ 3X-1 }{ x^2-1 }\)

  100. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    seems easier... :)

  101. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good! Would you like to do one while I'm offline, probably in less than 5 minutes?

  102. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sure i gotta go too xD

  103. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large \frac{3}{x-1}-\frac{2x}{x^2-1}\)

  104. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    huh? O_o

  105. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    http://prntscr.com/7bnxzi

  106. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Simplify \(\large \frac{3}{x-1}-\frac{2x}{x^2-1}\). Show work!

  107. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    im not sure how to do this .-.

  108. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I would factor the second denominator, x^2-1 into (x+1)(x-1) using difference of 2 squares (note 1=1^2). This gives \(\large \frac{3}{x-1}-\frac{2x}{(x+1)(x-1)}\) the proceed as before.

  109. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{3*x+1 }{ x-1*x+1 }-\frac{ 2x }{ (x+1)(x-1) }=\frac{ 6x(x+1) }{ (x^2-1 }\]

  110. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    A minor correction by adding parentheses: (using PEMBAS) \(\Large\frac{3*(x+1) }{ (x-1)*(x+1) }-\frac{ 2x }{ (x+1)(x-1) }=\frac{ 3x+3-2x }{ (x^2-1) }=?\)

  111. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The first step was perfect. Then you would distribute(expand) and add/subtract as needed. The final step I leave to you, if possible.

  112. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ew factoring

  113. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no wait

  114. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    in this case, there is nothing to factor! 3x-3-2x = 3x-2x-3=x-3 so answer is \(\Large \frac{x-3}{x^2-1}\)

  115. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i was gonna say that XD

  116. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    of course! I knew that! xD

  117. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lol u are learning all mai tricks >.>

  118. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, this is either called learning, or contamination, depending on the point of view! xD

  119. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    contamination >.> because now i cant use it :P

  120. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Spam!Spam!Spam!Spam!Spam!Spam!Spam!Spam!Spam!Spam!Spam! Spam!Spam!Spam!Spam!Spam!Spam!Spam!Spam!Spam!Spam!Spam!

  121. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    xD

  122. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just another contamination!

  123. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    LOL

  124. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok, would you feel sad if I say...

  125. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Are we done for the day? :o

  126. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Not at all

  127. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nope, but we're done with 11.2 to 11.6 ?

  128. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We are done? :o YAY NO MORE MATH

  129. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Not too fast, read the whole line, please! lol

  130. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So now we're onto Rational equations! Interesting stuff!

  131. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    T_T

  132. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Solve for x: \(\large x+1=\frac{72}{x}\)

  133. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i dont think i have learned this .-.

  134. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If not, now you will!

  135. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    O_O

  136. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wait im starting to remeber things >.>

  137. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Any idea where to start?

  138. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~\frac{ x+1 }{ 1}=\frac{ 72 }{ x }\]

  139. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent! Memories are coming back!

  140. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    next?

  141. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \huge~72*1=x(x+1)\] \[\huge~72=x^2+1x\]

  142. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent again! next?

  143. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~x^2+1x-72=0\]

  144. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Beautiful! Pray continue!

  145. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433116854133:dw| \[\huge~(x+9)(x-8)\]

  146. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're almost done. Equate each factor to zero to find the answers.

  147. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x=-9 x=8

  148. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    100% Excellent job!

  149. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think i have this section lets not do anymore :D ?

  150. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just two more! Solve for x: \(\large \frac{10}{x+4}=\frac{15}{4(x+1)}\) This is easier than FOIL.

  151. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    NO T_T

  152. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    There is no factoring involved, you'd do it in 10 seconds, + 30 minutes of typing.

  153. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~40(x+1)=15(x+4)\]

  154. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Too fast.... but everything is right!

  155. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    40x+40=15x+60 40x=15x+20 25x=20 x=20/25

  156. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent, and the answer is.....

  157. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x=20/25

  158. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ... or 4/5

  159. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    OR 20/25.

  160. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think most teachers would tolerate this (not simplifying), although I don't. I would give 95% instead of 100%. So it depends on your teacher!

  161. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    smh

  162. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're in trouble when I learn more of these! Well, you need to give extra credit to those who do a perfect job, that's my reasoning!

  163. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    xD

  164. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now the last one, you'd be sad when it's done!

  165. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    WAIT

  166. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    After this no more math??? :O

  167. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    T_T <---tears of joy

  168. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yeah, after this last problem, no more math (until your quiz) unless you have questions.

  169. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i have 2 questions on my hw thing i dont get at all : /

  170. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We'll look at that after this question. Perhaps by that time you will know how to do. Solve \(\large 3x=\frac{5x+6}{2x+3}\). Show work.

  171. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~\frac{ 3x }{ 1 }=\frac{ 5x+6 }{ 2x+3 }\] \[\huge3x(2x+3)=1(5x+6)\]

  172. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent, so far so good. You're living up to your reputations!

  173. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[6x^2+9x=5x+6\] \[6x^2+4x-6=0\] |dw:1433118120725:dw|

  174. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So far so good! Pray continue!

  175. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Actually, to make you life simpler, divide the equation by 2 to get 3x^2+2x-3=0 This will give smaller numbers, so easier to work with.

  176. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433118297396:dw|

  177. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    None.

  178. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent. What's the next step?

  179. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    idk

  180. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Quadratic formula!

  181. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    OMG NO T_T

  182. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So much work

  183. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lets just skip this one ;-; lets do one that doesnt have this

  184. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The reason I choose this one is because in the real world (including exams), answers don't always come out in integers.

  185. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just to make sure you're prepared for the quadratic formula. You could type the discriminant faster than lightning, why not the quad. formula?

  186. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What would the equation be?

  187. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :/

  188. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(6x^2+4x-6=0\), or half of that: 3x^2+2x-3 Either one will do, doesn't make a differce with the quad. formula. Makes a big diff. with factoring.

  189. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    a=3 b=2 c=-3 \[\huge~x=\frac{ -2 \pm \sqrt{(-2)^2-4(3)(-3)} }{ 2(3) } \]

  190. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Correct! Now pull out your calculator, or do it mentally, to find the final solution.

  191. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~x=\frac{ -2\pm~\sqrt{40} }{ 6 }\]

  192. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~x=\frac{ -2 \pm \sqrt{4\times10} }{ 6 }\]

  193. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~x=\frac{ -2 \pm 2\sqrt{10} }{ 6 }\]

  194. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, yours is correct (again 95%), unless ... \(\Large~x=\frac{ -2 \pm \sqrt{40} }{ 2(3) }\) \(\Large~x=\frac{ -1 \pm \sqrt{10} }{ 3 }\)

  195. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    T_T

  196. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lol, don't worry about the 5%, but I give you credit for coming that close, especially the part going from sqrt(40) to sqrt(10), excellent job!

  197. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

  198. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, in case you have nightmares with + and - signs poking at you, you can wake up and try this. It's not as hard as it seems. \(\Large \frac{3c}{c^2-4}+\frac{1}{c-2}=\frac{2}{c+2}\) You will need to simplify the left-hand side first, then do the equation solving.

  199. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    O_O where did u get that?

  200. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Does it look too difficult? BTW, the answer is -3, so you don't have to cheat! lol

  201. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    noo it looked fimiliar

  202. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Did you get it from your teacher? Well, I'll show you a gold mine. If you can't sleep, go to http://www.regentsprep.org/regents/math/algtrig/ate11/RationalEqPract.htm and practise all those problems!

  203. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    omg no way T_T

  204. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    With this one, do the simplification on the left-hand side and then solve. Do not follow the solution provided.

  205. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hmmmmk

  206. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You said you had two hw questions!

  207. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nvm :)

  208. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Can we practice more on everything once yr back? :)

  209. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sure!

  210. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ready. :)

  211. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @mathmate

  212. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Start with 11.2?

  213. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    or you have specific questions?

  214. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No lets just go with 11.2 etc

  215. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433125010350:dw| name the variation.

  216. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    inverse variation

  217. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good! x 1 2 3 4 5 y 2 4 6 8 10 what is x when y=14

  218. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    7? :/

  219. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yep, good!

  220. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x 1 5 10 y 20 4 2 What is y when x=40

  221. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    80

  222. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Hmmm....

  223. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    10?

  224. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We see that y is decreasing as x increases. See if you can find the rule!

  225. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    0

  226. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no, that's too small. The rule for direct variation is y=kx, where k is a constant. In the first example, x 1 2 3 4 5 y 2 4 6 8 10 we see that the rule is y=2x, so it is a direct variation.

  227. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The rule for inverse variation is y=k/x. For the second example, we have x 1 5 10 y 20 4 2 so the rule is y=20/x (20=20/1, 4=20/5, 2=20/10, ...) so what is y when x=40?

  228. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2

  229. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Another way to write the rule is xy=k For example 2, k=20, so 1*20=20 4*5=20...

  230. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    According to the rule, y=20/40 = 1/2, so when x=40, y=1/2 or use the alternate rule, xy=20 40y=20, or y=1/2

  231. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x 2 7 12 y 6 21 36 Name the variation, and find x when y=120

  232. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i dont like there >.>

  233. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    these

  234. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You've done those before?

  235. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I know we did not go over it, but never too late! :(

  236. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'll show a few examples first. Direct variation: rule y=kx (when x is greater, y is greater) Inverse variation: rule xy=k (when x increases, y decreases, that's why inverse) so far so good?

  237. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433125957505:dw|

  238. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Notice that inverse variation is not a straight line. It is a curve.

  239. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok so far?

  240. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yea

  241. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok, now, to find the rule, this is what you do.

  242. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    First find if the function is increasing, or decreasing. ok

  243. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you know how to tell if a function is increasing?

  244. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If the line is going up?

  245. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433126223857:dw|

  246. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes. An excellent example. If it is a straight line, we know it is not inverse.

  247. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Right :)

  248. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Is it automatically direct variation?

  249. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes? :/

  250. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Unfortunately, there are other variations. The one you drew is called a partial variation. It is a straight line that does not pass through the origin. A straight line that passes through the origin AND increasing, then it's direct!

  251. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Lets skip this.

  252. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433126603203:dw|

  253. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It has to do with the rule. A partial is y=mx+b where b\(\ne\)0 A direct is when y=kx (i.e. b=0) For example, x 2 5 8 y 6 12 18 is partial because y=2x+2 while x 2 5 8 y 4 10 16 is direct because y=2x

  254. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hmmmm makes a bit more sense :3

  255. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good! We'll get back to the last problem. x 2 7 12 y 6 21 36 Name the variation, state the rule, and find x when y=120

  256. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    T_T 120=k/x

  257. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you start with the variation? (is it increasing? If it is, it is not inverse)

  258. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    increasing .-.

  259. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so it cannot be inverse. The rule you gave is for inverse.

  260. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so y=mx+b?

  261. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    When you give a rule, you have to check that it works for at least two points.

  262. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    mm ;-; <---

  263. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and you need to find k. Let's say we decide that it is direct variation, then y=kx substitute (2,6) we have 6=2k, or k=3 Let's try it for another point: (12,36), so that is 36=12k, k=3 again. So we have found the rule y=3x. If y=120, then 120=3x, what is x?

  264. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    40

  265. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Exactly. So the rule is: 1. examine and assume a distribution. 2. substitute one of the points in the rule (of the assumed distribution) 3. check with another point, to see if the rule is still valid. 4. Give the answer.

  266. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    mmm k

  267. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now, try x 2 4 6 y 6 3 2 State 1. the variation 2. the rule 3. value of x when y=24

  268. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1) PArtial 2) y=mx+b 3) Lets skip it ;-;

  269. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, it's decreasing

  270. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so it is not direct. Is it a straight line, let's check the slope.

  271. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x 2 4 6 y 6 3 2 slope = (y2-y1)/(x2-x1) between 2 and 4, slope = (3-6)/(4-2) = -3/2 = -1.5 between 4 and 6, slope = (2-3)/(6-4) = 1/2 Since the slope is not constant, it is not a straight line.

  272. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So it's not partial. Try inverse: x 2 4 6 y 6 3 2 2*6=12 4*3=12 6*2=12 so k=12 for inverse!

  273. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you finish answering?

  274. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y=12x :/

  275. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Variation: inverse Rule: either xy=12, or y=12/x Now when y=24, what would x be?

  276. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2

  277. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Hin: Rule: either xy=12, or y=12/x

  278. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    weve spent about an hour on this .-. y=2? ??

  279. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    xy=12, y=24 so x=12/y=12/24=1/2 lol Yes, almost an hour.

  280. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and it was a good thing, because now you won't miss the easy questions.

  281. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @mathmate

  282. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    k, where do we go from here? (it's laggy)

  283. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Want to start a new post?

  284. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  285. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.