How do I go from:
$ \frac{3(1+0.2z^{-1})(1+z^{-1})}{(1+0.5z^{-1})(1-0.4z^{-1})} $
to
$ -3 + \frac{7}{1-0.4z^{-1}} - \frac{1}{1+0.5z^{-1}} $
I understand that the first form can be expanded as
$ \frac{A_1}{1-0.4z^{-1}} + \frac{A_2}{1+0.5z^{-1}} $
so the $7$ and $-1$ don't bother me, but I don't understand where the first term $(-3)$ in the second equation comes from.
Thank you