Answer
$\dfrac{x}{3}$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, then the given expression, $
\dfrac{2x}{5}\div\dfrac{6x+12}{5x+10}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2x}{5}\cdot\dfrac{5x+10}{6x+12}
\\\\=
\dfrac{2x}{5}\cdot\dfrac{5(x+2)}{6(x+2)}
\\\\=
\dfrac{\cancel{2}x}{\cancel{5}}\cdot\dfrac{\cancel{5}(\cancel{x+2})}{\cancel{2}\cdot3(\cancel{x+2})}
\\\\=
\dfrac{x}{3}
.\end{array}
