Answer
$\frac{(y+12)}{(y+15)}$
Work Step by Step
Since the numerator and the denominator both consist of a trinomial, we use the rules of factoring trinomials in order to factor them. Then, we cancel out the resultant common factors in the numerator and the denominator:
$\frac{y^{2}+20y+96}{y^{2}+23y+120}$
=$\frac{y^{2}+8y+12y+96}{y^{2}+8y+15y+120}$
=$\frac{y(y+8)+12(y+8)}{y(y+8)+15(y+8)}$
=$\frac{(y+8)(y+12)}{(y+8)(y+15)}$
=$\frac{(y+12)}{(y+15)}$
