# Thread: Partial Fraction Decomposition

1. ## 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!

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

Cross multiply by $\displaystyle (x^2+1)^2$ expand and equate coefficients wrt x. That will give you a system for A, B, C and D.

3. Hi

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

EDIT : too late !

4. Okay so my answer is (3x/x^2+1) + (x/(x^2+1)^2).

Is that right?

5. 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.