solution: 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 $x^2-9=0\Rightarrow x^2=9 \Rightarrow x=\pm3$. Thus, there are $\boxed{2}$ different values of $x$ that make the given expression undefined.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  For how many values of $x$ is the expression $\frac{x-5}{x^2-9}$  not defined?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 2
extra_info.question: For how many values of $x$ is the expression $\frac{x-5}{x^2-9}$  not defined?
extra_info.split: test