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Math Help - partial fractions

  1. #1
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    partial fractions

    how do I get the answer shown in the attached problem? when I tried it out, I couldn't get the numerator to 1.

    Thanks!
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  2. #2
    MHF Contributor Unknown008's Avatar
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    First, factor your denominator.

    remember that:

    a^2 - b^2 = (a+b)(a-b)

    Can you do it now?
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  3. #3
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    Quote Originally Posted by calculus0 View Post
    how do I get the answer shown in the attached problem? when I tried it out, I couldn't get the numerator to 1.

    Thanks!
    It will be easier to address your specific trouble if you show all of your working.
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  4. #4
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    We write

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

    With a bit of algebraic manipulation of the above equality(actually identity), we can find out that

     A = B = 1.(There are several ways to do this. One of them is writing the right hand side as a single fraction and we get an equation by equating the denominator with 2)

    So we have

    -1+\frac{2}{1-x^2} = -1 + \frac{2}{(1-x)(1+x)} = 1 +\frac{1}{1-x}+\frac{1}{1+x}_{.}
    Last edited by willy0625; June 8th 2010 at 12:38 AM.
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