Answer
See explanations.
Work Step by Step
We can write:
$\frac{f(x)}{2x-4}=\frac{1}{2}\times\frac{f(x)}{x-2}$
Which shows that dividing by $2x-4$ is equivalent to dividing by $x-2$ using synthetic division and then multiplying the result by $\frac{1}{2}$.