Example 13. Find the domain of the function $y=\frac{1}{\sqrt{x+1}-\sqrt{1-x}}$.
$$
\begin{array}{l}
\text { Sol } \because y=\frac{1}{\sqrt{x+1}-\sqrt{1-x}} \\
=\frac{\sqrt{x+1+\sqrt{1-x}}}{(x+1)-(1-x)}=\frac{\sqrt{x+1}+\sqrt{1-x}}{2 x}, \\
\therefore\left\{\begin{array} { l } 
{ x + 1 \geqslant 0 , } \\
{ 1 - x \geqslant 0 , } \\
{ x \neq 0 }
\end{array} \quad \left\{\begin{array}{l}
x \geqslant-1, \\
x \leqslant 1, \\
x \neq 0 .
\end{array}\right.\right.
\end{array}
$$

Sol $\because y=\frac{1}{\sqrt{x+1}-\sqrt{1-x}}$

Therefore, the domain of the function is: $-1 \leqslant x<0$ and $0<x \leqslant 1$.