Answer
$\frac{-a+8}{(a-4)(a-2)}$
Work Step by Step
First, we find a common denominator. This, upon inspection, is found to be $(a-4)(a-2)$. Then, we subtract the two fractions using this common denominator:
$\frac{2}{a-4}-\frac{3}{a-2}$
=$\frac{2(a-2)-3(a-4)}{(a-4)(a-2)}$
=$\frac{2a-4-3a+12}{(a-4)(a-2)}$
=$\frac{-a+8}{(a-4)(a-2)}$
