Simplify Complex Rational Expressions: example 8.50

$\begin{array}{cccc}& & & \hfill \frac{\frac{4}{y-3}}{\frac{8}{y^2-9}}\hfill \\ \\ \\ \text{Rewrite the complex fraction as division.}\hfill & & & \hfill \frac{4}{y-3}÷\frac{8}{y^2-9}\hfill \\ \\ \\ \begin{array}{c}\text{Rewrite as the product of first times the}\hfill \\ \text{reciprocal of the second.}\hfill \end{array}\hfill & & & \hfill \frac{4}{y-3}·\frac{y^2-9}{8}\hfill \\ \\ \\ \text{Multiply.}\hfill & & & \hfill \frac{4\left(y^2-9\right)}{8\left(y-3\right)}\hfill \\ \\ \\ \text{Factor to look for common factors.}\hfill & & & \hfill \frac{4\left(y-3\right)\left(y+3\right)}{4·2\left(y-3\right)}\hfill \\ \\ \\ \text{Remove common factors.}\hfill & & & \hfill \frac{\cancel{4}\cancel{\left(y-3\right)}\left(y+3\right)}{\cancel{4}·2\cancel{\left(y-3\right)}}\hfill \\ \\ \\ \text{Simplify.}\hfill & & & \hfill \frac{y+3}{2}\hfill \end{array}$

Are there any value(s) of $y$ that should not be allowed? The simplified rational expression has just a constant in the denominator. But the original complex rational expression had denominators of $y-3$ and $y^2-9$. This expression would be undefined if $y=3$ or $y=\mathrm{-3}$.