Example 6. Solve the equation $\sqrt{\frac{x+2}{x-1}}+\sqrt{\frac{x-1}{x+2}}=\frac{5}{2}$.
It is known that $x>1$ or $x<-2$, then the original equation $\stackrel{\text { Proposition } 2 \text { }}{\leftrightharpoons}$ $\Leftrightarrow$ $\sqrt{\frac{x+2}{x-1}}=2$ or $\sqrt{\frac{x+2}{x-1}}=\frac{1}{2}$, solving these yields $x_{1}=2, x_{2}=-3$ as the roots of the original equation.