Answer
$=\frac{4a+3}{5a-2}$
Work Step by Step
1. Factor the numerator
$= \frac{16a^{2}+24a+9}{20a^{2}+7a-6}$
$=\frac{16a^{2}+12a+12a+9}{20a^{2}+7a-6}$
$=\frac{4a(4a+3)+3(4a+3)}{20a^{2}+7a-6}$
$=\frac{(4a+3)(4a+3)}{20a^{2}+7a-6}$
2. Factor the denominator
$=\frac{(4a+3)(4a+3)}{20a^{2}+15a-8a-6}$
$=\frac{(4a+3)(4a+3)}{5a(4a+3)-2(4a+3)}$
$=\frac{(4a+3)(4a+3)}{(5a-2)(4a+3)}$
3. Cancel out $(4a+3)$ from the numerator and denominator:
$=\frac{(4a+3)}{(5a-2)}$
