I'm trying to evaluate the following integral: $$\oint_{|z_1|=1} \oint_{|z_2|=1} \frac{dz_1 dz_2}{z_1(z_2-1)(b(z_2+1)-1/2)+z_2(z_1-1)(a(z_1+1)-1/2)}$$ where a,b are real constants and $$ 1/4<a,b<1/2 $$ I know how to use the residual method in a one dimensional integral but I'm not sure how to use it in this case. I can see that we have a singularity when both parameters are $$ z_1=\frac{1}{2a}-1, z_2=\frac{1}{2b}-1 $$ at the same time. But how can I use it to solve the integral? Can someone please point me in the right direction or suggest relevant literature? How this type of integrals or subject would be called if I want to look up more info about it?
Thank you.