# Thread: Getting stuck with partial fractions

1. ## Getting stuck with partial fractions

Ok this is driving me nuts so I hope someone can help!

$\displaystyle 8s^2-4s+12/s(s^2+4)$

I am using partial fraction decomposition of this to find the A, B and C. So $\displaystyle 8s^2-4s+12=A/s +[B/(s-0)^2+4] +[C/(s-0)^2+4]$ and thus $\displaystyle 8s^2-4s+12=A[(s-0)^2+4]+Bs+Cs$

When I use the sub values in for S method, I am subbing in a 0 for the S, and this gets me 12=4A so A=3. BUT when you do it with the expand and compare method, I get A=8.

Where am I going wrong here??

2. $\displaystyle {12\over s(s^2+4)} = {3\over s} - {3s \over s^2 + 4}$. Or maybe you want $\displaystyle {8s^2-4s +12\over s(s^2+4)} = {3\over s} + {5s-4\over s^2 + 4}$, I can't really tell, sorry.

3. $\displaystyle \frac{8s^2-4s+12}{s(s^2+4)}=\frac{A}{s}+\frac{Bs+C}{s^2+4}=\f rac{3}{s}+\frac{5s-4}{s^2+4}$.
There is no solution for
$\displaystyle \frac{8s^2-4s+12}{s(s^2+4)}\ne\frac{A}{s}+\frac{B}{s^2+4}=\fr ac{A(s^2+4)+Bs}{s(s^2+4)}=\frac{As^2+Bs+4A}{s(s^2+ 4)}$
A=8
B=-4
4A=12 $\displaystyle \Rightarrow$ A=3
because the same time must be A=8 and A=3 what is impossible.