Answer
$\dfrac{5}{3x}$
Work Step by Step
The given expression, $
\dfrac{2x^3+16}{6x^2+12x}\cdot\dfrac{5}{x^2-2x+4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2(x^3+8)}{6x(x+2)}\cdot\dfrac{5}{x^2-2x+4}
\\\\=
\dfrac{2(x+2)(x^2-2x+4)}{6x(x+2)}\cdot\dfrac{5}{x^2-2x+4}
\\\\=
\dfrac{\cancel{2}(\cancel{x+2})(\cancel{x^2-2x+4})}{\cancel{2}\cdot3x(\cancel{x+2})}\cdot\dfrac{5}{\cancel{x^2-2x+4}}
\\\\=
\dfrac{5}{3x}
.\end{array}
