# Partial Fraction Decomposition

• Mar 28th 2009, 10:11 AM
ss103
Partial Fraction Decomposition
Find the partial fraction decomposition for the rational expression:
(3x^3+4x)/(x^2+1)^2

I know that you will have: A/? + B/? + C/? + D/? , but I don't know where to go from there.

Thanks!
• Mar 28th 2009, 10:16 AM
Jester
Quote:

Originally Posted by ss103
Find the partial fraction decomposition for the rational expression:
(3x^3+4x)/(x^2+1)^2

I know that you will have: A/? + B/? + C/? + D/? , but I don't know where to go from there.

Thanks!

$\frac{Ax+B}{x^2+1}+ \frac{Cx+D}{(x^2+1)^2} = \frac{3x^3+4x
}{(x^2+1)^2}$

Cross multiply by $(x^2+1)^2$ expand and equate coefficients wrt x. That will give you a system for A, B, C and D.
• Mar 28th 2009, 10:18 AM
running-gag
Hi

The form of the decomposition is $\frac{Ax+B}{x^2+1} + \frac{Cx+D}{(x^2+1)^2}$

EDIT : too late !
• Mar 28th 2009, 10:23 AM
ss103
Okay so my answer is (3x/x^2+1) + (x/(x^2+1)^2).

Is that right?
• Mar 28th 2009, 10:39 AM
Jester
Quote:

Originally Posted by ss103
Okay so my answer is (3x/x^2+1) + (x/(x^2+1)^2).

Is that right?

I got that too.