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Math Help - partial fraction from improper fraction

  1. #1
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    partial fraction from improper fraction

    Resolve into partial fractions:

    x^4 / (x^2 +1)(x^2 -1)


    sorry if it looks messy but im not sure how to make fractions, etc. on this forum



    anyway, since its a improper fraction i got the proper fraction by long devision and ended up with :

    1 + 1/ (x^2 +1)(x^2 -1)

    since i cant factorize (x^2 +1) how do i continue?

    do I just say A/(x^2 +1) + B/(x^2 -1) ?

    If so how do i calculate values if i have B(x^2 +1) ?
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  2. #2
    MHF Contributor

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    Quote Originally Posted by renaldo View Post
    Resolve into partial fractions:

    x^4 / (x^2 +1)(x^2 -1)


    sorry if it looks messy but im not sure how to make fractions, etc. on this forum



    anyway, since its a improper fraction i got the proper fraction by long devision and ended up with :

    1 + 1/ (x^2 +1)(x^2 -1)

    since i cant factorize (x^2 +1) how do i continue?

    do I just say A/(x^2 +1) + B/(x^2 -1) ?

    If so how do i calculate values if i have B(x^2 +1) ?
    If a denominator has an irreducble factor of the form x^2+ b^2, then its partial fraction decomposition will have a fraction of the form \frac{Ax+ B}{x^2+ b^2}

    \frac{1}{(x^2+1)(x^2-1)}= \frac{Ax+ B}{x^2+ 1}+ \frac{C}{x- 1}+ \frac{D}{x+ 1}.
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