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Math Help - [SOLVED] Partial Fraction Integration

  1. #1
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    Question [SOLVED] Partial Fraction Integration

    Evaluate the integral of 4/(1-x)(1+x)^2. the answer is supposed to be -2/x+1 + ln |x+1/x-1|

    I did A/1-x + B/1+x + C/1+x)^2 and eventually got this after multiplying by common denominators: -Bx^3+x^2(A-B)+x(2A+B-C)+A+B+C=1 and do not know how to solve for A, B, or C. Am I doing this right?
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  2. #2
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    This is too difficult to follow. Something like this would ideally be in Latex, but if you can't code it you have got to be clear with parentheses. It's a headache to look at, and that will discourage people from helping you. So if you clean it up I'll take another look. Maybe also include an intermediate steps. Again this makes things easier to follow and easier to spot errors.
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  3. #3
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    Red face

    sorry it's a mess...How do you do math code?
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  4. #4
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    Partial Fractions

    Hello juicysharpie
    Quote Originally Posted by juicysharpie View Post
    Evaluate the integral of 4/(1-x)(1+x)^2. the answer is supposed to be -2/x+1 + ln |x+1/x-1|

    I did A/1-x + B/1+x + C/1+x)^2 and eventually got this after multiplying by common denominators: -Bx^3+x^2(A-B)+x(2A+B-C)+A+B+C=1 and do not know how to solve for A, B, or C. Am I doing this right?
    \frac{4}{(1-x)(1+x)^2} = \frac{A}{1-x}+\frac{B}{1+x}+\frac{C}{(1+x)^2}

     = \frac{A(1+x)^2}{(1-x)(1+x)^2} +\frac{B(1-x)(1+x)}{(1-x) (1+x)^2}+\frac{C(1-x)}{(1-x)(1+x)^2}

    \Rightarrow A(1+x)^2+B(1-x)(1+x)+C(1-x) \equiv 4

    \Rightarrow A(1+2x+x^2)+B(1-x^2)+C(1-x) \equiv 4

    \Rightarrow x^2(A-B) + x(2A-C)+A+B+C \equiv 4

    Compare coefficients:

    A-B=0

    2A-C=0

    A+B+C=4

    \Rightarrow A=B=1, C=2

    Can you take it from here?

    Grandad

    PS If you want to see the Latex code behind any of these expressions, just click on them, and the code will open up in a separate window.
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  5. #5
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    Thumbs up

    Thanks for the help Grandad!! It was very nice of you to answer both of my questions.

    Thanks Jameson for the advice!
    Last edited by mr fantastic; February 11th 2009 at 03:53 AM. Reason: Merged posts
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  6. #6
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    Quote Originally Posted by juicysharpie View Post
    Thanks Jameson for the advice!
    I don't like making criticisms, but I'm glad you took it as advice.

    You should definitely look into learning Latex. The basic syntax is really easy. With a few commands you can insert symbols, radicals, fractions, exponents, etc. And if you get bored there is a lot of harder stuff to code. We have a whole forum devoted to Latex and it has a tutorial. You can see it on the main page.
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