1. The solution set of the inequality $\frac{20}{x-9}>\frac{22}{x-11}$ is
$$
\begin{array}{l}
\frac{10}{x-9}-\frac{11}{x-11}=\frac{10(x-11)-11(x-9)}{(x-9)(x-11)}=\frac{-x-11}{(x-9)(x-11)}>0 \\
\Rightarrow \frac{x+11}{(x-9)(x-11)}<0 \Rightarrow x<-11 \text { or } 9<x<11,
\end{array}
$$

Therefore, the solution set of the original inequality is $(-\infty,-11) \cup(9,11)$.