Answer
$\dfrac{3}{x+1}$
Work Step by Step
Factoring the given expression, $
\dfrac{x-8}{x^2-x-2}+\dfrac{2}{x-2}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{x-8}{(x-2)(x+1)}+\dfrac{2}{x-2}
.\end{array}
Using the $LCD=
(x-2)(x+1)
$, the expression above simplifies to
\begin{array}{l}
\dfrac{1(x-8)+(x+1)(2)}{(x-2)(x+1)}
\\\\=
\dfrac{x-8+2x+2}{(x-2)(x+1)}
\\\\=
\dfrac{3x-6}{(x-2)(x+1)}
\\\\=
\dfrac{3(x-2)}{(x-2)(x+1)}
\\\\=
\dfrac{3(\cancel{x-2})}{(\cancel{x-2})(x+1)}
\\\\=
\dfrac{3}{x+1}
.\end{array}
