Answer
$\dfrac{x(2x-9)}{(x+4)(x-3)(x-4)}$
Work Step by Step
The factored form of the given expression, $
\dfrac{3x}{x^2+x-12}-\dfrac{x}{x^2-16}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{3x}{(x+4)(x-3)}-\dfrac{x}{(x+4)(x-4)}
.\end{array}
Using the $LCD=
(x+4)(x-3)(x-4)
,$ the expression, $
\dfrac{3x}{(x+4)(x-3)}-\dfrac{x}{(x+4)(x-4)}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(x-4)(3x)-(x-3)(x)}{(x+4)(x-3)(x-4)}
\\\\=
\dfrac{3x^2-12x-x^2+3x}{(x+4)(x-3)(x-4)}
\\\\=
\dfrac{2x^2-9x}{(x+4)(x-3)(x-4)}
\\\\=
\dfrac{x(2x-9)}{(x+4)(x-3)(x-4)}
.\end{array}
