Answer
$\dfrac{2}{15-2x}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{1}{x}-\dfrac{2}{3x}}{\dfrac{5}{2x}-\dfrac{1}{3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{3(1)-1(2)}{3x}}{\dfrac{3(5)-2x(1)}{6x}}
\\\\=
\dfrac{\dfrac{3-2}{3x}}{\dfrac{15-2x}{6x}}
\\\\=
\dfrac{\dfrac{1}{3x}}{\dfrac{15-2x}{6x}}
\\\\=
\dfrac{1}{3x}\div\dfrac{15-2x}{6x}
\\\\=
\dfrac{1}{3x}\cdot\dfrac{6x}{15-2x}
\\\\=
\dfrac{1}{\cancel{3x}}\cdot\dfrac{\cancel{3x}\cdot2}{15-2x}
\\\\=
\dfrac{2}{15-2x}
.\end{array}