Determine the Laurent Series Expansion for the function
$$(z^2-1)\exp\left(\frac{2z}{z-1}\right)$$
at $a=1$ and find its ring of convergence.
I expanded the exponential function but I couldn't get it to work out properly. Any suggestions would be very appreciated. Thanks!
Hint: $$\frac{2z}{z-1}=2+\frac2{z-1}.$$ Plus, you know something about $\exp(u+v)$, right?