$$
\begin{array}{l}
\sqrt{5 \frac{5}{24}}=5 \sqrt{\frac{5}{24}} ; \\
\sqrt{12-\frac{12}{143}}=12 \sqrt{\frac{12}{143}} .
\end{array}
$$

4. Generalize the following correct equations into a general rule:
$$
\begin{array}{l}
\sqrt{5 \frac{5}{24}}=5 \sqrt{\frac{5}{24}} ; \\
\sqrt{12-\frac{12}{143}}=12 \sqrt{\frac{12}{143}} .
\end{array}
$$
4. The two known equations are special cases of the following general equation:
$$
\begin{array}{l} 
\sqrt{a+\frac{a}{a^{2}-1}}=\sqrt{\frac{a^{3}}{a^{2}-1}} \\
=a \sqrt{\frac{a}{a-2}} \quad(a>0, a \neq 1)
\end{array}
$$