How do I
(a) find the Laurent series for the following: $ f(z)=\frac {z^2+z+1}{(z-1)^2}$ (b) Find its pole and its order.
I suppose finding the Laurent series would make it easy to find the latter, but I think there's a short cut to finding the pole? Anyhow, I'm interested in both part (a) and part (b) above.
The only way I know to solve for part (a) is to use partial fractions, but in such a case I would still have a $(z-1)^2$ in one of the denominators since the above would split up as
$f(z)=(z^2+z+1)\left[\frac{A}{z-1} +\frac{B}{(z-1)^2}\right]$
Not sure how to proceed.