## anonymous one year ago Does anyone know how to add and subtract rational expressions? help very last assignment D:

1. anonymous

Its an assignment I have to do, but its all about adding and subtracting rational expression, only 5 problems

2. anonymous
3. anonymous

Hope this will help

4. anonymous

Ok c: Thanks

5. anonymous

My Pleasure.

6. anonymous

is it ok if i do one problem and show you to make sure im not doing anything wrong?

7. anonymous

@Nurali

8. UsukiDoll

post an example

9. UsukiDoll

I think the other user is afk or something

10. anonymous

ill draw a picture of it

11. anonymous

|dw:1433843733453:dw|

12. UsukiDoll

hmmm... they share a common denominator so all we have to do is to combine like terms in the numerator

13. anonymous

How would we do that? would we add 2x to x and 1 to the other 1?

14. UsukiDoll

yeah

15. anonymous

would the numerator come out like this = 2x^2+2 or 3x+2

16. UsukiDoll

it would be 3x+2. because 2x+x = 3x 1 + 1 =2

17. anonymous

Ok! thanks, can you help with four more adding/subracting q's?

18. UsukiDoll

sure

19. anonymous

Thankyou so much! so the next question basically wants me to use the answer we just got (3x+2/2x) subtracted by x/x+3, but it also says to * identify any possible restrictions that exist with (or in) the resulting rational expression*

20. UsukiDoll

$\frac{3x+2}{2x}-\frac{x}{x+3}$ it said any possible restrictions... so I"m not sure what that means 100% maybe what value makes the result undefined ?>! Not sure.. any way our lcd = (2x)(x+3) so we multiply x+3 on the first fraction and multiply 2x on the second fraction

21. anonymous

so like cross multiplying?

22. UsukiDoll

umm... similar but instead we need to find the least common denominator see example 3 on the cliffnotes site... noticed how they took the lcd of that problem?

23. anonymous

It looks kinda confusing sine the problem big :x

24. anonymous

on cliff notes

25. UsukiDoll

$\frac{3x+2}{2x} \times \frac{x+3}{x+3}-\frac{x}{x+3} \times \frac{2x}{2x}$

26. anonymous

ok that makes alot more since lol

27. UsukiDoll

example 3 on cliffnotes from Nurali was just x and y as the denominators. it was the later examples that I didn't choose because I knew it would be too much

28. anonymous

would we just times the bottom demonitaers togethor? like 2x(x+3)

29. UsukiDoll

yes...

30. UsukiDoll

$\frac{(3x+2)(x+3)-2x^2}{2x(x+3)}$ we have to remember that whenever we have a - sign on the right side of the equation, we need to distribute that sign all over

31. UsukiDoll

$-x(2x) \rightarrow -2x^2$

32. UsukiDoll

and we need to use FOIL method to expand the left side

33. anonymous

I know how to do that cx ill show you after im done foiling it c:

34. UsukiDoll

ok

35. anonymous

would we do the distributive property to the denomater? or does that stay the same

36. UsukiDoll

umm I think it depends on the numerator... because we wouldn't want to combine the denominator and end up that we can cancel something out...taking a step backwards

37. anonymous

i foiled the top but didn't add up yet, is this correct so far? 4x+9x+2x+6

38. UsukiDoll

$(3x+2)(x+3) -2x^2 = 3x^2+9x+2x+6 = 3x^2+11x+6 -2x^2 = x^2+11x+6$

39. UsukiDoll

remember $(x)(x) \rightarrow (x^1)(x^1) \rightarrow x^{1+1} \rightarrow x^2$

40. UsukiDoll

so... $(3x)(x) \rightarrow 3x^{1+1} \rightarrow 3x^2$

41. anonymous

Ohhh ok, so now i have x^2+11x-6/2x(x+3)

42. anonymous

would we cancel our the 6 from 3?

43. UsukiDoll

no

44. UsukiDoll

I don't think this can be factored... the only pairs for 6 is 6 x 1 1 x 6 2 x 3 3 x2 that's 6+1 =7 3+2 = 5 and subtracting will make it worse

45. anonymous

maybe thats the restrictions they talk about?

46. anonymous

i think

47. UsukiDoll

$\frac{x^2+11x-6}{2x(x+3)}$ maybe I wish it was more specific.. there is also what values of x makes this undefined too

48. UsukiDoll

2x(x+3) = 0 split into 2 problems 2x=0 x+3=0 solving x ... X = 0,-3

49. anonymous

those are probably the restrictions Cx , i think it does mean undifined

50. anonymous

ok so the next question wants me to do this |dw:1433845443996:dw|

51. UsukiDoll

$\frac{x^2+11x-6}{2x(x+3)} \times \frac{x+3}{x+1}$

52. anonymous

its x-1 cx

53. UsukiDoll

we can cancel out the x+3... it's in the numerator and denominator $\frac{x^2+11x-6}{2x(x+3)} \times \frac{x+3}{x-1}$

54. anonymous

oh true! so they would disapear?

55. UsukiDoll

YUP! :D

56. anonymous

yes! the easiest step on here lol cx so then the problem would be x^2+11-6/2 times x-1

57. anonymous

*divided by 2x not 2

58. anonymous

how would that work? since the second one isnt a denominater nor a numerator?

59. UsukiDoll

$\frac{x^2+11x-6}{2x} \times \frac{1}{x-1} \rightarrow \frac{x^2+11x-6}{2x(x-1)}$

60. UsukiDoll

huh?! ok wait I just latex the fractions without x+3 because the numerator had one and the denominator had one .

61. anonymous

ohhh ok i remebr learning that step now, so it would stay like that? :o

62. anonymous

what happened :o

63. UsukiDoll

what is the next question?

64. anonymous

you said they cancled eachother out cx, and now i have to divide that equation by 6/x-1, but it also says to (Discuss why the degree of the resulting denominator did not change from your expression’s degree)

65. UsukiDoll

$\frac{x^2+11x-6}{2x(x-1)}$ divided by $\frac{6}{x-1}$

66. anonymous

yea

67. UsukiDoll

if you flip the second fraction... surprise x-1 gets canceled out too.

68. UsukiDoll

$\frac{x^2+11x-6}{2x(x-1)} \times \frac{x-1}{6}$

69. anonymous

ohh and it turns into a mutplication by flipping?

70. UsukiDoll

when dividing fractions... you flip the second fraction... in the end you're multiplying

71. anonymous

Oh ok, that makes it easier cx

72. UsukiDoll

$\frac{x^2+11x-6}{2x} \times \frac{1}{6} \rightarrow \frac{x^2+11x-6}{12x}$

73. UsukiDoll

I think it's safe now to combine the denominator...

74. anonymous

oh yeah i keep forget that the single number would be on bottom and the 1 on top, and yea it does xD

75. anonymous

so then i would have to explain *Discuss why the degree of the resulting denominator did not change from your expression’s degree*

76. anonymous

what the flip does it mean by that lol :x

77. UsukiDoll

what is that?!

78. UsukiDoll

12x that's first degree isn't it?! awww c*** I haven't dealt with these questions in a while. pure math doesn't have this

79. anonymous

well we got the retrictions Q , and i just wanna finish this one assignemnt thingy lol, you look like your doing it right! cx its just these wierd Q's

80. UsukiDoll

how did it not change from the expression's degree? could it be referring to the original question?!

81. UsukiDoll

the first question you had ... contained 2x our fourth question had the denominator 2x(6) -> 12x I think they are the same first degree. That's just a guess ..

82. anonymous

maybe they mean degree by like * x, x^2, x^3

83. UsukiDoll

yeah I'm thinking that we compare the last answer we have to the first question? hmmmmmmmm?! the degrees are the same if we look at it that way?!

84. anonymous

haha yea, ill just say, i shouldnt get that many points taken off since were doing the rest right

85. anonymous

say that*

86. anonymous

Ok, so thats our final answer for Q 4, now we just have one left!

87. UsukiDoll

o-o I thought that was the final one?!

88. anonymous

no this one is the final one lol,

89. anonymous

90. anonymous

4* i mean

91. UsukiDoll

????????????

92. anonymous

93. UsukiDoll

ok

94. anonymous

|dw:1433847285555:dw|

95. anonymous

its that one^

96. UsukiDoll

ok first combine the second and third fraction

97. anonymous

i meant subract 6

98. anonymous

not + and ok cx

99. anonymous

2x/2x+2 ?

100. UsukiDoll

|dw:1433847473742:dw|

101. UsukiDoll

x + x = 2x .. the denominator stays the same..... OMG EVEN I DID +6 #FAIL

102. anonymous

I|dw:1433847507052:dw|

103. anonymous

lol its, its late at night lol xD

104. UsukiDoll

$\frac{x^2+11x-6}{12x} + \frac{2x}{x+1}$

105. UsukiDoll

now use the least common denominator which is 12x(x+1)

106. anonymous

so we would do that whole timezing the first by the equation and the second by the second one?

107. UsukiDoll

but only multiply what is misssing for the first fraction we have 12x.. x+1 is missing so multiply x+1/x+1

108. UsukiDoll

$\frac{x^2+11x-6}{12x} \times \frac{x+1}{x+1} + \frac{2x}{x+1} \times\frac{2x}{2x}$

109. UsukiDoll

OOPS

110. anonymous

wait, so why did we mutiply 2x instead of 12?

111. UsukiDoll

cuz I typoed

112. UsukiDoll

$\frac{x^2+11x-6}{12x} \times \frac{x+1}{x+1} + \frac{2x}{x+1} \times\frac{12x}{12x}$

113. anonymous

ok lol, and for example on the first bottom ones we would do (12x)(x+1) ?

114. UsukiDoll

yeah

115. UsukiDoll

numerator on the left is going to be a bit tough though

116. anonymous

ok :x ill do the denomnaters and show u

117. anonymous

|dw:1433847901459:dw|

118. UsukiDoll

|dw:1433847957533:dw|

119. UsukiDoll

$(x^2+11x-6)(x+1) = x^3+11x^2-6x+x^2+11x-6 = x^3+12x^2+5x-6$

120. UsukiDoll

$x^3+12x^2+5x-6+24x^2 = x^3+36x^2+5x-6$

121. UsukiDoll

$\frac{x^3+36x^2+5x-6}{12x(x+1)}$

122. anonymous

is that the end point? xO

123. anonymous

or do we do stuff with the denomatr to the numerator now?

124. UsukiDoll

hmmm... I think that's it?!

125. UsukiDoll

we can't use factor by grouping with the numerator

126. UsukiDoll

not a perfect cube either

127. anonymous

yea, it should be lol i cant belive 4 problems took an hour :X, and thank you soOO much! i've asked this Q many times on here and noone has helped me like you have! and yea it doesnt look like a perfect cube

128. UsukiDoll

I think it was due to my latex writing too.. that takes a bit of time and thinking xD

129. anonymous

i dont think so cx these types of Q's look like theyd take forever lol, and we were moving pretty fast cx

130. anonymous

again thank you so muccccch! very appreciated that you helped me cx

131. UsukiDoll

:D