Answer
$\frac{15x-9}{(x-2)(x+1)}$
Work Step by Step
By inspection, we see that the LCM of the denominators is $(x-2)(x+1)$. Therefore, we create a common denominator using this LCM and obtain:
$\frac{7}{x-2}+\frac{8}{x+1}$
=$\frac{7(x+1)+8(x-2)}{(x-2)(x+1)}$
=$\frac{7x+7+8x-16}{(x-2)(x+1)}$
=$\frac{15x-9}{(x-2)(x+1)}$
