Example 7. Solve the equation for $x$:
$$
\sqrt{\frac{a-x}{b+x}}+{ }^{n} \sqrt{\frac{b+x}{a-x}}=2.
$$
$$
(a>b>0)
$$
It is known that $-\mathrm{b}b>0, \therefore-b$ $<\frac{1}{2}(a-b)<a$, so $x=\frac{1}{2}(a-b)$ is a root of the original equation.