What is the domain of the real-valued function $f(x)=\frac{2x-7}{\sqrt{x^2-5x+6}}$?
\(x^2-5x+6\ge 0 \)
\((x-2)(x-3)\ge 0 \iff x\le 2,\ x\ge 3\)
or \(\boxed{x \in (-\infty, 2] \cup [3, \infty)}\)