Answer
$\dfrac{34-9x}{15x-30}$
Work Step by Step
Factoring the given expression, $ \dfrac{5}{3x-6}-\dfrac{x}{x-2}+\dfrac{3+2x}{5x-10} ,$ results to \begin{array}{l}\require{cancel} \dfrac{5}{3(x-2)}-\dfrac{x}{x-2}+\dfrac{3+2x}{5(x-2)} .\end{array} Using the $LCD= 15(x-2) $, the expression above simplifies to \begin{array}{l}
\dfrac{5(5)-15(x)+3(3+2x)}{15(x-2)}
\\\\=
\dfrac{25-15x+9+6x}{15(x-2)}
\\\\=
\dfrac{34-9x}{15(x-2)}
\\\\=
\dfrac{34-9x}{15x-30}
.\end{array}
