Answer
$\dfrac{3}{x}$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, then the given expression, $
\dfrac{7}{3x}\div\dfrac{14-7x}{18-9x}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{7}{3x}\cdot\dfrac{18-9x}{14-7x}
\\\\=
\dfrac{7}{3x}\cdot\dfrac{9(2-x)}{7(2-x)}
\\\\=
\dfrac{\cancel{7}}{\cancel{3}x}\cdot\dfrac{\cancel{3}\cdot3(\cancel{2-x})}{\cancel{7}(\cancel{2-x})}
\\\\=
\dfrac{3}{x}
.\end{array}
