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Math Help - Partial Fraction Decomposition

  1. #1
    djr
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    Partial Fraction Decomposition

    Hi,

    I'm stuck on a problem that requires partial fraction decomposition:

    2 / [(x2 + 1)( x2 + 4)]

    I can't figure out what to do about the x-squared form in the denominator.

    edit: I guess those exponents didn't format right. Can someone point me to some info on displaying equations in a pretty, math-ish type way?
    Last edited by djr; April 17th 2008 at 10:16 AM.
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  2. #2
    MHF Contributor red_dog's Avatar
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    \displaystyle\frac{2}{(x^2+1)(x^2+4)}=\frac{Ax+B}{  x^2+1}+\frac{Cx+D}{x^2+4}=
    \displaystyle=\frac{(A+C)x^3+(B+D)x^2+(4A+C)x+4B+D  }{(x^2+1)(x^2+4)}
    Then
    \displaystyle\left\{\begin{array}{c}A+C=0\\B+D=0\\  4A+C=0\\4B+D=2\end{array}\right. \Rightarrow A=C=0, B=\frac{2}{3}, D=-\frac{2}{3}
    So, \displaystyle\frac{2}{(x^2+1)(x^2+4)}=\frac{2}{3}\  left(\frac{1}{x^2+1}-\frac{1}{x^2+4}\right)
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  3. #3
    djr
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    Aha, that makes sense. I'm used to only needing A and B. Thank You.
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