Answer
$\dfrac{m+6}{m+3}$
Work Step by Step
The given expression, $
\dfrac{m^2+3m+2}{m^2+5m+4}\div\dfrac{m^2+5m+6}{m^2+10m+24}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{m^2+3m+2}{m^2+5m+4}\cdot\dfrac{m^2+10m+24}{m^2+5m+6}
\\\\=
\dfrac{(m+2)(m+1)}{(m+4)(m+1)}\cdot\dfrac{(m+4)(m+6)}{(m+2)(m+3)}
\\\\=
\dfrac{(\cancel{m+2})(\cancel{m+1})}{(\cancel{m+4})(\cancel{m+1})}\cdot\dfrac{(\cancel{m+4})(m+6)}{(\cancel{m+2})(m+3)}
\\\\=
\dfrac{m+6}{m+3}
.\end{array}
