problem: For how many values of $x$ is the function $y=\frac{x-2}{x^2-7x+10}$ not defined?
solution: By factoring the denominator, the equation becomes \[y=\frac{x-2}{(x-2)(x-5)}.\]The function is not defined when the denominator is 0, which occurs at $x = 2$ and $x = 5$.  Therefore, there are $\boxed{2}$ values of $x$ for which the function is not defined.