Answer
$\dfrac{(2x-3)(6+x)}{6x^2}$
Work Step by Step
The given expression, $
\left( \dfrac{2}{3}-\dfrac{1}{x} \right)\cdot\left( \dfrac{3}{x}+\dfrac{1}{2} \right)
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x(2)-3(1)}{3x}\cdot\dfrac{2(3)+x(1)}{2x}
\\\\
\dfrac{2x-3}{3x}\cdot\dfrac{6+x}{2x}
\\\\
\dfrac{(2x-3)(6+x)}{6x^2}
.\end{array}
