Partial fraction decomposition trouble I'm trying to do a partial fraction expansion on
$$Y = n \cdot \frac{e^{-pt_{0}}}{(p+n)(p^2+\omega^2)}$$
which gives $A(p^2+\omega^2)+(Bp+C)(p+n) = 1$
which implies 
$$A = -B$$
$$Bpn=0\rightarrow B=0\rightarrow A=0$$
which is incorrect. Any help with what I'm missing would be greatly appreciated

The condition
$$
A(p^2 + \omega^2) + (B p + C)(p + n ) = 1
$$
leads to the equations
\begin{eqnarray}
A + B &=& 0 \\
B n + C &=& 0 \\
A \omega^2 +  C n &=& 1
\end{eqnarray}
whose solution is
\begin{eqnarray}
A &=& \frac{1}{\omega^2 + n^2} = -B \\
C &=& \frac{n}{\omega^2 + n^2}  
\end{eqnarray}
So the fraction is
$$
Y = \frac{n e^{-pt_0}}{\omega^2 + n^2}\left[ \frac{1}{p + n} + \frac{n-p}{p^2 + \omega^2} \right]
$$
