Answer
$\dfrac{7(x-4)}{2(x-2)}$
Work Step by Step
The given expression, $
\dfrac{7x+28}{2x+4}\div\dfrac{x^2+2x-8}{x^2-2x-8}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{7x+28}{2x+4}\cdot\dfrac{x^2-2x-8}{x^2+2x-8}
\\\\=
\dfrac{7(x+4)}{2(x+2)}\cdot\dfrac{(x-4)(x+2)}{(x+4)(x-2)}
\\\\=
\dfrac{7(\cancel{x+4})}{2(\cancel{x+2})}\cdot\dfrac{(x-4)(\cancel{x+2})}{(\cancel{x+4})(x-2)}
\\\\=
\dfrac{7(x-4)}{2(x-2)}
.\end{array}
