Question

divide the following rational expression.
\\(\frac{y^{2}-9}{y - 3}div\frac{y + 3}{4y - 12}\\)

select the correct choice below and fill in the answer box to complete your choice.
(simplify your answer )
\\(\bigcirc\\) a. \\(\frac{y^{2}-9}{y - 3}div\frac{y + 3}{4y - 12}=\square, y\
eq - 3,3\\)
\\(\bigcirc\\) b. \\(\frac{y^{2}-9}{y - 3}div\frac{y + 3}{4y - 12}=\square, y\
eq - 3, - 4,12\\)

Explanation:

Step1: Rewrite division as multiplication

$\frac{y^2 - 9}{y - 3} \times \frac{4y - 12}{y + 3}$

Step2: Factor all polynomials

$y^2-9=(y-3)(y+3)$, $4y-12=4(y-3)$
Substitute: $\frac{(y-3)(y+3)}{y - 3} \times \frac{4(y-3)}{y + 3}$

Step3: Cancel common factors

Cancel $(y-3)$ and $(y+3)$:
$\frac{\cancel{(y-3)}\cancel{(y+3)}}{\cancel{y - 3}} \times \frac{4(y-3)}{\cancel{y + 3}} = 4(y-3)$

Step4: Identify restricted values

Denominators can't be 0:

1. $y-3

eq0 \implies y
eq3$

1. $4y-12

eq0 \implies y
eq3$

1. $y+3

eq0 \implies y
eq-3$
So $y
eq-3,3$

Answer:

A. $\frac{y^{2}-9}{y-3}\div \frac{y+3}{4y-12}=4(y-3), y
eq -3,3$