Answer
$\dfrac{5(x+3)}{4(4x-5)}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{x+3}{12}}{\dfrac{4x-5}{15}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x+3}{12}\div\dfrac{4x-5}{15}
\\\\=
\dfrac{x+3}{12}\cdot\dfrac{15}{4x-5}
\\\\=
\dfrac{x+3}{\cancel{3}\cdot4}\cdot\dfrac{\cancel{3}\cdot5}{4x-5}
\\\\=
\dfrac{5(x+3)}{4(4x-5)}
.\end{array}
