2. Given the sets $A=\left\{x \mid x^{2}-3 x+2 \leqslant 0\right\}, B=\left\{x \left\lvert\, \frac{1}{x-3}<a\right.\right\}$, if $A \subseteq B$, then the range of real number $a$ is


$A=[1,2] \Rightarrow \frac{1}{x-3} \in\left[-1,-\frac{1}{2}\right] \Rightarrow a>-\frac{1}{2}$, so the range of values for $a$ is $\left(-\frac{1}{2},+\infty\right)$.