Answer
$\dfrac{5(a-2)}{7}$
Work Step by Step
The given expression, $
\dfrac{5a^2-20}{a^3+2a^2+a+2}\div\dfrac{7a}{a^3+a}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{5a^2-20}{a^3+2a^2+a+2}\cdot\dfrac{a^3+a}{7a}
\\\\=
\dfrac{5(a^2-4)}{(a^3+2a^2)+(a+2)}\cdot\dfrac{a(a^2+1)}{7a}
\\\\=
\dfrac{5(a+2)(a-2)}{a^2(a+2)+(a+2)}\cdot\dfrac{a(a^2+1)}{7a}
\\\\=
\dfrac{5(a+2)(a-2)}{(a+2)(a^2+1)}\cdot\dfrac{a(a^2+1)}{7a}
\\\\=
\dfrac{5(\cancel{a+2})(a-2)}{(\cancel{a+2})(\cancel{a^2+1})}\cdot\dfrac{\cancel{a}(\cancel{a^2+1})}{7\cancel{a}}
\\\\=
\dfrac{5(a-2)}{7}
.\end{array}
