Answer
$\dfrac{2x^2+19x-5}{(3x-1)(x-4)(x+2)}$
Work Step by Step
Factoring the given expression, $
\dfrac{2x}{3x^2-13x+4}+\dfrac{5}{x^2-2x-8}
,$ results to
\begin{array}{l}
\dfrac{2x}{(3x-1)(x-4)}+\dfrac{5}{(x-4)(x+2)}
.\end{array}
Using the $LCD=
(3x-1)(x-4)(x+2)
$, the expression above simplifies to
\begin{array}{l}
\dfrac{(x+2)(2x)+(3x-1)(5)}{(3x-1)(x-4)(x+2)}
\\\\=
\dfrac{2x^2+4x+15x-5}{(3x-1)(x-4)(x+2)}
\\\\=
\dfrac{2x^2+19x-5}{(3x-1)(x-4)(x+2)}
.\end{array}
