9.085. $0.2^{\frac{x^{2}+2}{x^{2}-1}}>25$.
Solution.

Domain of definition: $\quad x \neq \pm 1$.

Rewrite the inequality as

$5^{-\frac{x^{2}+2}{x^{2}-1}}>5^{2} \Leftrightarrow-\frac{x^{2}+2}{x^{2}-1}>2, \frac{x^{2}+2}{x^{2}-1}+2<0, \frac{x^{2}+2+2 x^{2}-2}{x^{2}-1}<0$,

$\frac{3 x^{2}}{x^{2}-1}<0,\left\{\begin{array}{l}x \neq 0, \\ x^{2}-1<0\end{array} \Leftrightarrow\left\{\begin{array}{l}x \neq 0, \\ -1<x<1 .\end{array}\right.\right.$

Answer: $\quad x \in(-1 ; 0) \cup(0 ; 1)$