Answer
$\dfrac{-x+17}{(x-2)(x+3)}$
Work Step by Step
Using the $LCD=
(x-2)(x+3)
$, the given expression, $
\dfrac{3}{x-2}-\dfrac{4}{x+3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(x+3)(3)-(x-2)(4)}{(x-2)(x+3)}
\\\\=
\dfrac{3x+9-4x+8}{(x-2)(x+3)}
\\\\=
\dfrac{-x+17}{(x-2)(x+3)}
.\end{array}
