\displaystyle{f(z) = \frac{1}{(z^2 - 1)(z^2 + 4) } = \frac{1}{5}\cdot (\frac{1}{z^2 - 1} - \frac{1}{z^2+4}) = \frac{1}{5}\cdot ( \frac{1}{2} \cdot ( \frac{1}{z-1} - \frac{1}{z+1}) - \frac{1}{4i} \cdot (\frac{1}{z-2i} - \frac{1}{z+2i}))}