Answer
$2$
Work Step by Step
The given expression, $
\dfrac{\dfrac{2}{x+5}+\dfrac{4}{x+3}}{\dfrac{3x+13}{x^2+8x+15}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{2(x+3)+4(x+5)}{(x+5)(x+3)}}{\dfrac{3x+13}{(x+3)(x+5)}}
\\\\=
\dfrac{\dfrac{2(x+3)+4(x+5)}{\cancel{(x+5)(x+3)}}}{\dfrac{3x+13}{\cancel{(x+5)(x+3)}}}
\\\\=
\dfrac{2(x+3)+4(x+5)}{3x+13}
\\\\=
\dfrac{2x+6+4x+20}{3x+13}
\\\\=
\dfrac{6x+26}{3x+13}
\\\\=
\dfrac{2(3x+13)}{3x+13}
\\\\=
\dfrac{2(\cancel{3x+13})}{\cancel{3x+13}}
\\\\=
2
.\end{array}
