Show that the map $w(z)=\frac{1}{1-z^2}$ is a Conformal Mapping..

Question

Show that the mapping $$w(z)=\frac{1}{1-z^2}$$ is a Conformal Mapping.

My try-

$$w(z)=\frac{1}{1-z^2}$$ $$ w'(z)=\frac{2z}{(1-z^2)^2}$$ $$ w'(z)\neq 0 \ \forall\ z\neq 0$$ So $w(z)$ is a Conformal Map for all $z\neq 0$ . What happens at $0, 1,-1$?