Answer
$\dfrac{4a+12}{2a-10}\div\dfrac{a^{2}-9}{a^{2}-a-20}=\dfrac{2(a+4)}{a-3}$
Work Step by Step
$\dfrac{4a+12}{2a-10}\div\dfrac{a^{2}-9}{a^{2}-a-20}$
Factor both rational expressions completely:
$\dfrac{4a+12}{2a-10}\div\dfrac{a^{2}-9}{a^{2}-a-20}=\dfrac{4(a+3)}{2(a-5)}\div\dfrac{(a-3)(a+3)}{(a-5)(a+4)}=...$
Evaluate the division of the two fractions:
$...=\dfrac{4(a+3)(a-5)(a+4)}{2(a-5)(a-3)(a+3)}=...$
Simplify by removing the factors that appear both in the numerator and in the denominator:
$...=\dfrac{4(a+4)}{2(a-3)}=\dfrac{2(a+4)}{a-3}$
