I want to integrate $\displaystyle \int\_\gamma \frac{z}{(z-1)(z-2)}dz$ along the curve $\gamma(t)=2+\frac{1}{2}e^{it}$, with $t\in [0,2\pi]$

Can this be done by mean of residues? The curve is not closed, so I think it might be a problem. The fact that exercise was in a chapter calleed "Cauchy integral formula and residues" suggest that this theorems should be used to solve the integral