Does $\frac{\ln((z-a)(z-b))}{(z-a)(z-b)}$ have a residue at $z=a$?

Question

For $a,b>0$ and $b>a+1$, consider the contour integral

$$\oint_{|z|=a+\epsilon}\frac{\ln((z-a)(z-b))}{(z-a)(z-b)}dz.$$

This essentially corresponds to taking the residue at $z=a$. What does this result in?