Answer
$\dfrac{4a^2}{a-b}$
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{a+b}{ab}\div\dfrac{a^2-b^2}{4a^3b}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{a+b}{ab}\cdot\dfrac{4a^3b}{a^2-b^2}
\\\\=
\dfrac{a+b}{ab}\cdot\dfrac{ab\cdot4a^2}{(a-b)(a+b)}
\\\\=
\dfrac{\cancel{a+b}}{\cancel{ab}}\cdot\dfrac{\cancel{ab}\cdot4a^2}{(a-b)(\cancel{a+b})}
\\\\=
\dfrac{4a^2}{a-b}
.\end{array}
