Question

(\frac{y^2 - 9}{(y - 3)(y + 2)})\\(\frac{(quad)(quad)}{(y - 3)(y + 2)})

Explanation:

Step1: Factor numerator (difference of squares)

Recall $a^2 - b^2 = (a-b)(a+b)$. For $y^2 - 9$, $a=y$, $b=3$.
$y^2 - 9 = (y-3)(y+3)$

Step2: Substitute factored form

Replace $y^2 -9$ with its factored equivalent.
$\frac{(y-3)(y+3)}{(y-3)(y+2)}$

Answer:

The filled-in numerator is $\boldsymbol{(y-3)(y+3)}$