Given $$\int_{\gamma}\frac{1}{(z-a)(z-\frac{1}{a})}dz,$$ and $0, where $\gamma(t)=e^{it}$ and $0\le t \le 2\pi$
I am trying to find the residue of$$f(z)=\frac{1}{(z-a)(z-\frac{1}{a})}$$
The answer says $\operatorname{res}(f,\mathbb C)=\frac{1}{(a-\frac{1}{a})}$?
Any help will be appreciated, thanks.