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??