Answer
$\dfrac{3x^2+23x-7}{(2x-1)(x-5)(x+3)}$
Work Step by Step
Factoring the given expression, $
\dfrac{3x}{2x^2-11x+5}+\dfrac{7}{x^2-2x-15}
,$ results to
\begin{array}{l}
\dfrac{3x}{(2x-1)(x-5)}+\dfrac{7}{(x-5)(x+3)}
.\end{array}
Using the $LCD=
(2x-1)(x-5)(x+3)
$, the expression above simplifies to
\begin{array}{l}
\dfrac{(x+3)(3x)+(2x-1)(7)}{(2x-1)(x-5)(x+3)}
\\\\=
\dfrac{3x^2+9x+14x-7}{(2x-1)(x-5)(x+3)}
\\\\=
\dfrac{3x^2+23x-7}{(2x-1)(x-5)(x+3)}
.\end{array}
