Residue of $\frac{i}{(z-2)(2z-1)}$ at $z=1/2$

Question

Trying to do this but can't seem to figure out where I'm going wrong.

\begin{align*} \textrm{Res}(f,1/2) &= \frac{i}{\frac{1}{2}-2}\\ &= -\frac{2}{3}i \end{align*}

The correct answer however is $-i/3$.

Answer 1

$\lim_{z \to \frac 1 2} (z-\frac 1 2) \frac i {(z-2)(2z-1)}=\lim_{z \to \frac 1 2} \frac i {2(z-2)}=-\frac i 3$.