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anonymous

  • 5 years ago

simplify complex fractions:

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  1. amistre64
    • 5 years ago
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    complex as in with the imaginary "i"?

  2. anonymous
    • 5 years ago
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    all you need to know is i^2 = -1

  3. anonymous
    • 5 years ago
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    no mutiplying and dividing rational expressions \[(x^3y^2z)/(a^2b^2)/(a^3x^2y)/(b^2)\]

  4. anonymous
    • 5 years ago
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    where the slash is its written like a fraction

  5. anonymous
    • 5 years ago
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    So what is over what here?

  6. anonymous
    • 5 years ago
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    stack the parenthisis up ontop of each other where it looks like a fraction with things. idk how to punch it in on here were it looks like it does on my worksheet

  7. amistre64
    • 5 years ago
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    you can use // to mean the main divider bar between them, or some other version like */* just explain the symbol :)

  8. anonymous
    • 5 years ago
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    From what it looks like, I would assume it's like a rational expression over another. Correct?

  9. amistre64
    • 5 years ago
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    the b^2.s cancel out

  10. anonymous
    • 5 years ago
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    yes rational expressions

  11. amistre64
    • 5 years ago
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    basic strategy as with all fraction on fraction math is to turn the bottom one upside down and multiply across... 1/5 // 6/3 = 1/5 * 3/6 = 3/30

  12. anonymous
    • 5 years ago
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    but when its all letters and exponets how do you do it

  13. amistre64
    • 5 years ago
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    you mean the multiply part? or the flipping part?

  14. anonymous
    • 5 years ago
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    the multiply part. flipping i get now but idk what to do with the letters

  15. amistre64
    • 5 years ago
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    make it easier on yourself and split them up... a^4 means aaaa c^2 mean cc r^7 means rrrrrrr

  16. amistre64
    • 5 years ago
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    now, x^3 times x^4 means xxx xxxx = xxxxxxx = x^7

  17. amistre64
    • 5 years ago
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    c^4 times c^5 means cccc ccccc = ccccccccc = c^9

  18. anonymous
    • 5 years ago
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    yea i get the x^4 means xxxx but what about x^3y^2z

  19. amistre64
    • 5 years ago
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    xxx yy z is all that is

  20. amistre64
    • 5 years ago
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    squish em all together, then count them back out again....

  21. anonymous
    • 5 years ago
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    what your confusing me

  22. anonymous
    • 5 years ago
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    a/x = a* 1/x, therefore \[(x ^{3}y ^{2}z)/(a ^{2}b ^{2})/(a ^{2} x ^{2} y)/(b ^{2})] = \[(x ^{3} y ^{2} z)/(a ^{2} b2) * 1/(a ^{2} x ^{2} y)/(b ^{2})] = \[(x ^{3} y ^{2} z)/(a ^{2} b ^{2})*(b^{2})/(a ^{2} x ^{2} y)\]

  23. amistre64
    • 5 years ago
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    xxx yy z bb -------- x ------ aa bb aaa xx y

  24. amistre64
    • 5 years ago
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    anything that is the same on the top and bottom can be tossed out, it just means it equals 1. x y z 1 x y z xyz ----- x ---- = ------ = ---- aa aaa aaaaa a^5

  25. anonymous
    • 5 years ago
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    still not makin a whole lota sense

  26. amistre64
    • 5 years ago
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    which part is not making sense?

  27. amistre64
    • 5 years ago
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    i flipped it, you said thatpart you understood.... whats left?

  28. amistre64
    • 5 years ago
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    Does: xx y bb ------ = 1? xx y bb

  29. anonymous
    • 5 years ago
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    the whole thing. its a fraction placed ontop on a fraction saying simplify. like am i supposed to add the exponets together, flip them and multiply, or flip and divide

  30. amistre64
    • 5 years ago
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    flip the bottom, thats always the first step. split the exponents up so you can see what you got whatever is the same from top to bottom cancels out to 1 squish the rest together and number them again with an exponent.

  31. amistre64
    • 5 years ago
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    lets keep it simpler, how would I start this? x^2/y^3 // y/x^2

  32. anonymous
    • 5 years ago
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    flip it and take away the x^2 and just leave it as xy^3/xy i think

  33. amistre64
    • 5 years ago
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    one step at a time, dont rush ahead... lets flip the bottom x^2 x^2 ---- * ---- now what do I do? y^3 y

  34. anonymous
    • 5 years ago
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    the x^2 ---- y part

  35. anonymous
    • 5 years ago
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    oh wait y^3 x y ------- x^2 x^2

  36. amistre64
    • 5 years ago
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    you let me worry about making it look good on the screen, just tell me what we do next...

  37. amistre64
    • 5 years ago
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    I already flipped it, x^2 x^2 ---- * ---- now what do I do? y^3 y

  38. anonymous
    • 5 years ago
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    i want to say crossmultiply

  39. anonymous
    • 5 years ago
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    but thats usually not with letter

  40. amistre64
    • 5 years ago
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    we do that if there is an (=) between them, there is no (=) here so we dont "cross" multilply, we just multiply straight across

  41. anonymous
    • 5 years ago
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    ok just add the exponets together

  42. amistre64
    • 5 years ago
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    -------------->> x^2 x^2 x^2 x^2 ---- * ---- = ---------- y^3 y y^3 y -------------->> does this look right to you?

  43. anonymous
    • 5 years ago
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    not really shouldnt it be x^3/y^4

  44. amistre64
    • 5 years ago
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    not yet.... but does the setup look right? did I multiply it across correctly?

  45. anonymous
    • 5 years ago
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    yea i think.

  46. amistre64
    • 5 years ago
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    now lets add exponents to get the final result x^2 x^2 x^(2+2) x^4 ------- = --------- = ---- y^2 y y^(2+1) y^4

  47. amistre64
    • 5 years ago
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    2+1 = 3... sorry, forgot how to add :)

  48. anonymous
    • 5 years ago
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    that looks more like it

  49. amistre64
    • 5 years ago
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    so lets try your original problem and see if we can step thru it ok?

  50. anonymous
    • 5 years ago
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    ok

  51. amistre64
    • 5 years ago
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    x^3 y^2 z --------- a^2 b^2 --------------- a^3 x^2 y -------- b^2 our first step is to do what?

  52. anonymous
    • 5 years ago
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    im working it on a sheet of paper and the first thing i did was put the bottom fraction beside it and put a division sign between them

  53. amistre64
    • 5 years ago
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    ok.... x^3 y^2 z a^3 x^2 y --------- / ---------- a^2 b^2 b^2 now what?

  54. anonymous
    • 5 years ago
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    um flip the entire thing upside down or add the exponets

  55. amistre64
    • 5 years ago
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    only flip the right side fraction... not the "whole" problem....JUST that right side gets flipped. right?

  56. anonymous
    • 5 years ago
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    ok

  57. amistre64
    • 5 years ago
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    just like this.... x^3 y^2 z b^2 --------- ---------- a^2 b^2 a^3 x^2 y

  58. anonymous
    • 5 years ago
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    yea then add the exponets together

  59. amistre64
    • 5 years ago
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    what do you mean by add the exponents together? that is not really something that needs to be done just yet. Look at the top and the bottom of this oversized fraction and see if we can cross out stuff that looks the same.

  60. amistre64
    • 5 years ago
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    lets "line" things up from top to bottom....are we allowed to do that?

  61. anonymous
    • 5 years ago
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    line things up idk what your talking about

  62. amistre64
    • 5 years ago
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    I am going to move the stuff around so that it looks better. Like this..... x^3 y^2 z b^2 -------------------- x^2 y a^2 a^3 b^2

  63. amistre64
    • 5 years ago
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    what can you see that we can "get rid of" that is the same from the top and the bottom?

  64. anonymous
    • 5 years ago
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    um on the bottom combine the a^2 and a^3 together to get a^5

  65. amistre64
    • 5 years ago
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    good we can do that... x^3 y^2 z b^2 -------------------- x^2 y a^5 b^2

  66. anonymous
    • 5 years ago
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    can we also combine the x^3 and x^2 or not since there on seperate parts of the equation

  67. amistre64
    • 5 years ago
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    we cant "add" them together but watch this: xx x ---- = what? xx

  68. anonymous
    • 5 years ago
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    5

  69. amistre64
    • 5 years ago
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    no....not quite. do you remember that anything when placed over itself is equal to 1? 2 -- = 1 2 6m --- = 1 6m xx -- = 1 xx

  70. anonymous
    • 5 years ago
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    i think

  71. amistre64
    • 5 years ago
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    this is a fundamental concept in math. whenever we "divide" a number by itself we get an answer of 1 1 --- 8 | 8 right?

  72. anonymous
    • 5 years ago
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    i guess but i dont particularly see how that would work in this type of problem

  73. amistre64
    • 5 years ago
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    all fractions are is division. what is 1 divided by 2 = 1/2 3 divided by 5 = 3/5 15 divided by 5 = 15/5 all fractions are division......

  74. amistre64
    • 5 years ago
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    when we divide a number by itself we get 1 9 divided by 9 = 9/9 = 1

  75. anonymous
    • 5 years ago
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    but in this case were dividing x^3/ x^2

  76. amistre64
    • 5 years ago
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    exactly :) which is why I like to split it up so that you can "see" what is going on with exponents. x x x xx x ---- = --- -- = 1x = x x x xx 1

  77. anonymous
    • 5 years ago
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    so like that i can just "get rid of" the x part in the equation

  78. amistre64
    • 5 years ago
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    not the whole thing... but you can get rid of alot of x s how many x's do I have left in my solution up there?

  79. anonymous
    • 5 years ago
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    the x^3 and the x^2 so 5 i think

  80. amistre64
    • 5 years ago
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    x x x xx x ---- = --- -- = 1x = x x x xx 1 ^ how many x's do I have right here?

  81. anonymous
    • 5 years ago
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    1

  82. amistre64
    • 5 years ago
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    then we are left with 1 lonely little x that we have to leave in this equation.... right?

  83. anonymous
    • 5 years ago
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    yea

  84. amistre64
    • 5 years ago
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    you know already that we we multiply exponents we "add" then together. When we do the opposite of multiplication (which is division) we do the opposite to the exponents too. we "SUBTRACT them. x^3/x^2 = x^(3-2) = x^1 = x

  85. anonymous
    • 5 years ago
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    ok so how do we plug this one lonely x into the equation

  86. amistre64
    • 5 years ago
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    we just put it back were we got it from :) like this: x y^2 z b^2 ------------- y a^5 b^2

  87. anonymous
    • 5 years ago
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    ok what next. same thing to the b^2s

  88. amistre64
    • 5 years ago
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    yep, that would be good. b^2/b^2 is division.... so we SUBTRACT exponents. b^(2-2) = b^0 = 1 which just disappears

  89. anonymous
    • 5 years ago
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    ok so the b is just slapped onto the end of the top part of the equation without the exponent on it

  90. amistre64
    • 5 years ago
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    there is no b to put back if b^3 means bbb and b^1 means b b^0 means _______ no little b's to do anything with, zero b's, they are gone......

  91. anonymous
    • 5 years ago
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    so on the actual equation after this last part the b will be no more

  92. amistre64
    • 5 years ago
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    thats correct, they vanished...... x y^2 z --------- now whats left to work with? y a^5

  93. anonymous
    • 5 years ago
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    the y

  94. amistre64
    • 5 years ago
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    very good :) so, can you show me how we work that out?

  95. anonymous
    • 5 years ago
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    y^2/y^19(which is just nothing) subtract them and it leaves y

  96. amistre64
    • 5 years ago
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    perfect!!

  97. amistre64
    • 5 years ago
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    x y z ------ we appear to have come to the end :) a^5

  98. anonymous
    • 5 years ago
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    that 9 wasnt supposed to be there my finger sliped off the shift button when i hit the paraenthasis

  99. amistre64
    • 5 years ago
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    i figured that :)

  100. anonymous
    • 5 years ago
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    weird stinkin keyboards

  101. amistre64
    • 5 years ago
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    i start getting so many typos it looks like im having a stroke......

  102. anonymous
    • 5 years ago
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    back during the first of march i was in germany on a school junior senior trip and their keyboard was all kinds of weird

  103. amistre64
    • 5 years ago
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    Yep different places have different setups for their own uses. But this is the answer to our original problem.... x y z ------ a^5

  104. amistre64
    • 5 years ago
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    I just want to go over one little detail.....

  105. anonymous
    • 5 years ago
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    ok

  106. amistre64
    • 5 years ago
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    when dividing with exponents, it is important to notice where the biggest one is. For example: x^3/x^2 has the bigger number on top, so our answer goes back on top. BUT if the bottom has the bigger exponent, our answer will go back on the bottom. for example: x^2/x^7 has the bottom bigger than the top, we subtract like before but when were done our leftovers go on the bottom. Does that make sense?

  107. anonymous
    • 5 years ago
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    yea location of the bigger exponet is where the outcome of the division goes

  108. amistre64
    • 5 years ago
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    very good :) Ciao

  109. anonymous
    • 5 years ago
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    thank you so much if i have anymore questions ill just post them up and maybe be able to catch ya

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