Calculus with Applications (10th Edition)

$\dfrac{m^{2}+3m+2}{m^{2}+5m+4}\div\dfrac{m^{2}+5m+6}{m^{2}+10m+24}=\dfrac{m+6}{m+3}$
$\dfrac{m^{2}+3m+2}{m^{2}+5m+4}\div\dfrac{m^{2}+5m+6}{m^{2}+10m+24}$ 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: $...=\dfrac{m+6}{m+3}$