I have a signal $h[n]=\frac{1}{z+3}$ and the solution is $H(z) = (-3)^{n-1}\delta[n-1]$.
Looking the solution up in a transformation table, I come to the conclusion that I need to transform $h[n]$ to look like this:
$$h[n]=\frac{z^{-1}}{z^{-1}+3}$$
But I can't figure out how to accomplish this.