Answer
$\dfrac{5x-2}{(x-3)(x+2)(x-2)}$
Work Step by Step
The factored form of the given expression, $
\dfrac{3}{x^2-x-6}+\dfrac{2}{x^2-5x+6}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{3}{(x-3)(x+2)}+\dfrac{2}{(x-3)(x-2)}
.\end{array}
Using the $LCD=
(x-3)(x+2)(x-2)
,$ the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(x-2)(3)+(x+2)(2)}{(x-3)(x+2)(x-2)}
\\\\=
\dfrac{3x-6+2x+4}{(x-3)(x+2)(x-2)}
\\\\=
\dfrac{5x-2}{(x-3)(x+2)(x-2)}
.\end{array}
