Partial Fraction Decomposition

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March 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!
March 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!

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

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.
March 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 !
March 28th 2009, 10:23 AM
ss103

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

Is that right?
March 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.

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