# Math Help - Partial Fraction Decomposition

1. ## Partial Fraction Decomposition

Hi,

I'm stuck on a problem that requires partial fraction decomposition:

2 / [(x2 + 1)( x2 + 4)]

I can't figure out what to do about the x-squared form in the denominator.

edit: I guess those exponents didn't format right. Can someone point me to some info on displaying equations in a pretty, math-ish type way?

2. $\displaystyle\frac{2}{(x^2+1)(x^2+4)}=\frac{Ax+B}{ x^2+1}+\frac{Cx+D}{x^2+4}=$
$\displaystyle=\frac{(A+C)x^3+(B+D)x^2+(4A+C)x+4B+D }{(x^2+1)(x^2+4)}$
Then
$\displaystyle\left\{\begin{array}{c}A+C=0\\B+D=0\\ 4A+C=0\\4B+D=2\end{array}\right. \Rightarrow A=C=0, B=\frac{2}{3}, D=-\frac{2}{3}$
So, $\displaystyle\frac{2}{(x^2+1)(x^2+4)}=\frac{2}{3}\ left(\frac{1}{x^2+1}-\frac{1}{x^2+4}\right)$

3. Aha, that makes sense. I'm used to only needing A and B. Thank You.