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