Answer
$\dfrac{7x^2-9x-13}{(2x+1)(x-5)(3x-2)}$
Work Step by Step
The factored form of the given expression, $
\dfrac{2x-1}{2x^2-9x-5}+\dfrac{x+3}{6x^2-x-2}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{2x-1}{(2x+1)(x-5)}+\dfrac{x+3}{(2x+1)(3x-2)}
.\end{array}
Using the $LCD=
(2x+1)(x-5)(3x-2)
,$ the solution/s of the given equation is/are
\begin{array}{l}\require{cancel}
\dfrac{(2x-1)(3x-2)+(x-5)(x+3)}{(2x+1)(x-5)(3x-2)}
\\\\
\dfrac{(6x^2-4x-3x+2)+(x^2+3x-5x-15)}{(2x+1)(x-5)(3x-2)}
\\\\
\dfrac{(6x^2-7x+2)+(x^2-2x-15)}{(2x+1)(x-5)(3x-2)}
\\\\
\dfrac{7x^2-9x-13}{(2x+1)(x-5)(3x-2)}
.\end{array}
