#### Answer

$\dfrac{3}{x}$

#### Work Step by Step

The given expression, $
\left( \dfrac{1}{2}+\dfrac{2}{x} \right) - \left( \dfrac{1}{2}-\dfrac{1}{x} \right)
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x(1)+2(2)}{2x} - \dfrac{x(1)-2(1)}{2x}
\\\\
\dfrac{x+4}{2x} - \dfrac{x-2}{2x}
\\\\
\dfrac{x+4-(x-2)}{2x}
\\\\
\dfrac{x+4-x+2}{2x}
\\\\
\dfrac{6}{2x}
\\\\
\dfrac{\cancel{2}\cdot3}{\cancel{2}x}
\\\\
\dfrac{3}{x}
.\end{array}