## anonymous 4 years ago Partial fraction decomposition

1. anonymous

$3x^{2} \over x^{3}-4x$

2. anonymous

oh wait i am a moron! start with $\frac{3x}{(x+2)(x-2)}$ because one of the x's cancels!!

3. anonymous

then it is much easier, write $\frac{3x}{(x+2)(x-2)}=\frac{a}{x+2}+\frac{b}{x-2}$ and then $a(x-2)+b(x+2)=3x$ and solve for a and b

4. anonymous

for example, replace x by 2 and get $4b=6$ so $b=\frac{3}{2}$ and replace x by -2 toget $-4a=-6$ and therefore $x=-\frac{3}{2}$