Answer
$\dfrac{m^{2}+3m+2}{m^{2}+5m+4}\div\dfrac{m^{2}+5m+6}{m^{2}+10m+24}=\dfrac{m+6}{m+3}$
Work Step by Step
$\dfrac{m^{2}+3m+2}{m^{2}+5m+4}\div\dfrac{m^{2}+5m+6}{m^{2}+10m+24}$
Factor both rational expressions completely:
$\dfrac{m^{2}+3m+2}{m^{2}+5m+4}\div\dfrac{m^{2}+5m+6}{m^{2}+10m+24}=...$
$...=\dfrac{(m+2)(m+1)}{(m+4)(m+1)}\div\dfrac{(m+3)(m+2)}{(m+6)(m+4)}=...$
Evaluate the division of the two rational expressions:
$...=\dfrac{(m+2)(m+1)(m+6)(m+4)}{(m+4)(m+1)(m+3)(m+2)}=...$
Simplify the resulting expression by removing the factors that appear both in the numerator and in the denominator:
$...=\dfrac{m+6}{m+3}$
