jmc

The expression is not defined when the denominator is equal to zero. Thus, we need to find the number of values of $x$ such that $x^2-9=0$. Rearranging the equation and taking the square root of both sides, we have $x^2-9=0\Rightarrow x^2=9\Rightarrow x=\pm 3$. Thus, there are $\boxed{2}$ different values of $x$ that make the given expression undefined.