El_Arrow
  • El_Arrow
i need help with partial fractions problem
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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El_Arrow
  • El_Arrow
\[\frac{ 2x }{ (x-1)^3 }\]
El_Arrow
  • El_Arrow
@zepdrix @ganeshie8
zepdrix
  • zepdrix
You have a repeated linear factor in the denominator: \(\large\rm (x-1)\) is linear. So do you remember how to break that down? I'll give an example:\[\large\rm \frac{4x+2}{(x+1)^2}=\frac{A}{x+1}+\frac{B}{(x+1)^2}\]And then you would solve for A and B.

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zepdrix
  • zepdrix
\[\large\rm \frac{2x}{(x-1)^3}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C}{(x-1)^3}\]Understand the initial setup? :O
El_Arrow
  • El_Arrow
yeah
El_Arrow
  • El_Arrow
i used x=1 and got 2 for c is it correct?
zepdrix
  • zepdrix
mmm yah that sounds right! :)
El_Arrow
  • El_Arrow
getting the other 2 looks complicated
zepdrix
  • zepdrix
Hmm I think I see a neat trick for the other ones :) Obviously we'd like to avoid expanding everything right?
El_Arrow
  • El_Arrow
yeah
El_Arrow
  • El_Arrow
okay let me try
zepdrix
  • zepdrix
Oh I made a boo boo.. my bad :( \(\large\rm A\ne B\) I forgot about the C=2 part on the end, woooops.. back up :O
zepdrix
  • zepdrix
Back to the drawing board >.< woops woops
zepdrix
  • zepdrix
I still like the idea of plugging in x=0, and x=-1 it will give you a system of 2 equations with A and B.
zepdrix
  • zepdrix
It's probably about the same amount of work as expanding though
El_Arrow
  • El_Arrow
well i have the final answer at the back of the book and its |dw:1442723235969:dw|
El_Arrow
  • El_Arrow
so c is not equal to 2
zepdrix
  • zepdrix
Really? Hmm wolfram is saying that we should have c=2 and b=2 https://www.wolframalpha.com/input/?i=partial+fraction+decomposition+%282x%29%2F%28x-1%29%5E3
zepdrix
  • zepdrix
maybe typo in the book :O
El_Arrow
  • El_Arrow
i guess there is a typo in the book
El_Arrow
  • El_Arrow
so how does it get B=2?
zepdrix
  • zepdrix
I keep running into mistakes when I try to plug values in. I'm just gonna expand it out and see if we can get the right values...
El_Arrow
  • El_Arrow
okay im gonna try that too
zepdrix
  • zepdrix
\[\large\rm 2x=A(x-1)^2+B(x-1)+C\]\[\large\rm 2x=A(x-1)^2+B(x-1)+2\]\[\large\rm 2x=A(x^2-2x+1)+B(x-1)+2\]\[\large\rm 2x=Ax^2-2Ax+A+Bx-B+2\]Then, matching up the squares,\[\large\rm 0x^2=Ax^2\qquad\implies\qquad 0=A\]Matching up the first degree terms,\[\large\rm 2x=-2Ax+Bx\qquad\implies\qquad 2=-2A+B\]And matching up the constant terms,\[\large\rm 0=A-B+2\]
El_Arrow
  • El_Arrow
so |dw:1442723741155:dw|
El_Arrow
  • El_Arrow
thanks for helping me figuring this one out
zepdrix
  • zepdrix
Ya I guess we shoulda just expanded from the beginning D: wasn't as tough as i thought it would be

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