Chapter 7 - Section 7.6 - Radical Equations and Problem Solving - Exercise Set - Page 456: 87

$\dfrac{x}{4x+3}$

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