Answer
$-\dfrac{5}{18}$
Work Step by Step
The factored form of the given expression, $
\dfrac{5x+2}{-6}\div\dfrac{15x+6}{5}
,$ is
\begin{align*}
\dfrac{5x+2}{-6}\div\dfrac{3(5x+2)}{5}
.\end{align*}
Multiplying by the reciprocal of the divisor, the expression above is equivalent to
\begin{align*}\require{cancel}
&
\dfrac{5x+2}{-6}\cdot\dfrac{5}{3(5x+2)}
\\\\&=
\dfrac{\cancel{5x+2}}{-6}\cdot\dfrac{5}{3(\cancel{5x+2})}
\\\\&=
\dfrac{1}{-6}\cdot\dfrac{5}{3}
\\\\&=
\dfrac{5}{-18}
\\\\&=
-\dfrac{5}{18}
.\end{align*}
