How to Simplify Partial Fraction Decomposition with Complex Roots?

[matematikuvol]

Homework Statement

How to get partial fraction decomposition for
$$\frac{1}{(x^2+a^2)(x^2+p^2)}$$

Homework Equations

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?

Homework Statement

 

[Mark44]

Homework Statement

How to get partial fraction decomposition for
$$\frac{1}{(x^2+a^2)(x^2+p^2)}$$

Homework Equations

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?

Homework Statement

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.