Answer
$2$
Work Step by Step
The given expression, $ \dfrac{\dfrac{2}{x+2}+\dfrac{6}{x+7}}{\dfrac{4x+13}{x^2+9x+14}} ,$ simplifies to \begin{array}{l}\require{cancel}
\dfrac{\dfrac{2(x+7)+6(x+2)}{(x+2)(x+7)}}{\dfrac{4x+13}{(x+2)(x+7)}}
\\\\=
\dfrac{\dfrac{2(x+7)+6(x+2)}{\cancel{(x+2)(x+7)}}}{\dfrac{4x+13}{\cancel{(x+2)(x+7)}}}
\\\\=
\dfrac{2(x+7)+6(x+2)}{4x+13}
\\\\=
\dfrac{2x+14+6x+12}{4x+13}
\\\\=
\dfrac{8x+26}{4x+13}
\\\\=
\dfrac{2(4x+13)}{4x+13}
\\\\=
\dfrac{2(\cancel{4x+13})}{\cancel{4x+13}}
\\\\=
2
.\end{array}
