2. Solve the inequality $\frac{\sqrt{x^{2}-5}}{x}-\frac{x}{\sqrt{x^{2}-5}}<\frac{5}{6}$. (8 points)
Solution: Domain of definition: $|x|>\sqrt{5} . \frac{\sqrt{x^{2}-5}}{x}-\frac{x}{\sqrt{x^{2}-5}}\sqrt{5}$ inequality is true.
2) For $x<6$, or $\left(-x \sqrt{x^{2}-5}\right)^{2}>36$,

$$
\begin{aligned}
& x^{4}-5 x^{2}-36>0,\left(x^{2}+4\right)\left(x^{2}-9\right)>0,(x+3)(x-3)>0 \text{. Since } x<-\sqrt{5} \text{, then } \\
& x<-3 . \quad \text { Answer: } x \in(-\infty ;-3) \cup(\sqrt{5} ;+\infty) \text{. }
\end{aligned}
$$