Answer
$\dfrac{2m^{2}-5m-12}{m^{2}-10m+24}\div\dfrac{4m^{2}-9}{m^{2}-9m+18}=\dfrac{m-3}{2m-3}$
Work Step by Step
$\dfrac{2m^{2}-5m-12}{m^{2}-10m+24}\div\dfrac{4m^{2}-9}{m^{2}-9m+18}$
Factor both rational expressions completely:
$\dfrac{2m^{2}-5m-12}{m^{2}-10m+24}\div\dfrac{4m^{2}-9}{m^{2}-9m+18}=...$
$...=\dfrac{(2m+3)(m-4)}{(m-6)(m-4)}\div\dfrac{(2m+3)(2m-3)}{(m-6)(m-3)}=...$
Evaluate the division of the two fractions:
$...=\dfrac{(2m+3)(m-4)(m-6)(m-3)}{(m-6)(m-4)(2m+3)(2m-3)}=...$
Simplify by removing the factors that appear both in the numerator and in the denominator of the resulting rational expression:
$...=\dfrac{m-3}{2m-3}$
