I am trying to find the singular points, toe pole type and compute the residue of: 
$$\frac{\sinh(z)}{z^4(1-z^2)}$$
With $z\_0=0$ I am ok since it is easy to find the residue by Laurent expansion (it is a principal pole. Am i right? infinite times in the denominator).

But with $z=1$and $z=-1$ I have a problem. How can I compute the Laurent expansion around 1 and -1? Also are $z=1$, $z=-1$ simple poles?

Thanks!