## Elementary Algebra

$=\frac{4a+3}{5a-2}$
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: $=\frac{(4a+3)}{(5a-2)}$