Answer
$=\displaystyle \frac{2(5x-14)}{(x-2)(x-3)}, \quad x\neq 2,3$
Work Step by Step
The denominators are different.
Find a common denominator.
LCD=$(x-2)(x-3)$
$\displaystyle \frac{8}{x-2}+\frac{2}{x-3}= \displaystyle \frac{8(x-3)}{(x-2)(x-3)}+\frac{2(x-2)}{(x-2)(x-3)}$
$=\displaystyle \frac{8x-24+2x-4}{(x-2)(x-3)}$
$=\displaystyle \frac{10x-28}{(x-2)(x-3)}$
$=\displaystyle \frac{2(5x-14)}{(x-2)(x-3)}$
... exclude values that yield 0 in the denominator:
$x\neq 2,3$
... and, cancel common factors (here, there are none)
$=\displaystyle \frac{2(5x-14)}{(x-2)(x-3)}, \quad x\neq 2,3$
