Answer
$\dfrac{5}{2x}$
Work Step by Step
Factoring the given expression, $
\dfrac{5}{x^2-3x}\div\dfrac{4}{2x-6}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{5}{x(x-3)}\div\dfrac{4}{2(x-3)}
.\end{array}
Multiplying by the reciprocal of the divisor and cancelling common factors between the numerator and the denominator, the expression above simplifies to
\begin{array}{l}
\dfrac{5}{x(x-3)}\cdot\dfrac{2(x-3)}{4}
\\\\=
\dfrac{5}{x(\cancel{x-3})}\cdot\dfrac{\cancel{2}(\cancel{x-3})}{\cancel{2}\cdot2}
\\\\=
\dfrac{5}{2x}
.\end{array}
