To find out when the expression is not defined, I need to look at the denominator and see when it is equal to zero. So I'll set $x^2-9=0$ and solve for $x$. This is a quadratic equation, so I can use the difference of squares formula to factor it as $(x-3)(x+3)=0$. Then, by the zero product property, either $x-3=0$ or $x+3=0$. So the solutions are $x=3$ and $x=-3$. These are the values of $x$ that make the denominator zero and the expression undefined. There are two of them, so the answer is 2. 
For how many values of $x$ is the expression $\frac{x-5}{x^2-9}$  not defined?