# Homework Help: Partial fraction

1. Dec 11, 2012

### matematikuvol

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

2. Relevant equations

3. The attempt at a solution
I tried with
$$\frac{1}{(x+ia)(x-ia)(x+ip)(x-ip)}=\frac{A}{x+ia}+\frac{B}{x-ia}+\frac{C}{x-ip}+\frac{D}{x+ip}$$
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. Dec 11, 2012

### 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.