2. Solve the inequality $\frac{\sqrt{x^{2}-16}}{x}-\frac{x}{\sqrt{x^{2}-16}}<\frac{16}{15}$. (8 points)
Solution: Domain of definition: $|x|>4 . \frac{\sqrt{x^{2}-16}}{x}-\frac{x}{\sqrt{x^{2}-16}}4$ inequality is true.
2) For $x15$, or $\left(-x \sqrt{x^{2}-16}\right)^{2}>225$,

$$
\begin{aligned}
& x^{4}-16 x^{2}-225>0,\left(x^{2}+9\right)\left(x^{2}-25\right)>0,(x+5)(x-5)>0 \text{. Since } x<-4 \text{, then } \\
& x<-5 . \quad \text{ Answer: } x \in(-\infty ;-5) \cup(4 ;+\infty) \text{. }
\end{aligned}
$$