Answer
$\dfrac{2(x-1)}{x+6}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{x^2+5x-6}{4x+3}}{\dfrac{(x+6)^2}{8x+6}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{(x+6)(x-1)}{4x+3}}{\dfrac{(x+6)(x+6)}{2(4x+3)}}
\\\\=
\dfrac{(x+6)(x-1)}{4x+3}\div\dfrac{(x+6)(x+6)}{2(4x+3)}
\\\\=
\dfrac{(x+6)(x-1)}{4x+3}\cdot\dfrac{2(4x+3)}{(x+6)(x+6)}
\\\\=
\dfrac{(\cancel{x+6})(x-1)}{\cancel{4x+3}}\cdot\dfrac{2(\cancel{4x+3})}{(\cancel{x+6})(x+6)}
\\\\=
\dfrac{2(x-1)}{x+6}
.\end{array}
