2. Solve the inequality $\sqrt{\frac{x-24}{x}}-\sqrt{\frac{x}{x-24}}<\frac{24}{5}$.
Solution:

$\sqrt{\frac{x-24}{x}}-\sqrt{\frac{x}{x-24}}<0 ; \frac{1}{y}-y<0 ;$

$y_{1,2}=\frac{-12 \pm 13}{5}, y_{1}=\frac{1}{5}, y_{2}=-5$. Thus $y>\frac{1}{5}, \frac{x}{x-24}>\frac{1}{25} \Leftrightarrow \frac{x+1}{x-24}>0 \Leftrightarrow\left[\begin{array}{l}x<-1 \\ x>24\end{array}\right.$

Answer: $x \in(-\infty ;-1) \cup(24 ;+\infty)$.