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Partial fraction

  1. Dec 11, 2012 #1
    1. The problem statement, all variables and given/known data
    How to get partial fraction decomposition for
    [tex]\frac{1}{(x^2+a^2)(x^2+p^2)}[/tex]


    2. Relevant equations






    3. The attempt at a solution
    I tried with
    [tex]\frac{1}{(x+ia)(x-ia)(x+ip)(x-ip)}=\frac{A}{x+ia}+\frac{B}{x-ia}+\frac{C}{x-ip}+\frac{D}{x+ip}[/tex]
    and get the result at the end of the day. Is there some easiest way to handle this problem?
    1. The problem statement, all variables and given/known data
     
  2. jcsd
  3. Dec 11, 2012 #2

    Mark44

    Staff: Mentor

    Since the two factors in the denominator are irreducible quadratics, I would decompose the original fraction like this:

    $$\frac{1}{(x^2+a^2)(x^2+p^2)} = \frac{Ax + B}{x^2+a^2} + \frac{Cx + D}{x^2+p^2}$$

    Note that A and a represent different numbers.
     
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