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