The discussion focuses on simplifying partial fraction decomposition for the expression \(\frac{1}{(x^2+a^2)(x^2+p^2)}\). Participants suggest using the form \(\frac{Ax + B}{x^2+a^2} + \frac{Cx + D}{x^2+p^2}\) to handle irreducible quadratic factors in the denominator. This method is confirmed as effective for obtaining the decomposition without resorting to complex roots. The approach streamlines the process compared to using linear factors derived from complex roots.
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matematikuvol said: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