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