Answer
$\dfrac{5x-2}{(x-3)(x+2)(x-2)}$
Work Step by Step
The given expression, $ \dfrac{3}{x^2-x-6}+\dfrac{2}{x^2-5x+6} ,$ simplifies to \begin{array}{l}\require{cancel}
\dfrac{3}{(x-3)(x+2)}+\dfrac{2}{(x-2)(x-3)}
\\\\=
\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}
