Example. Solve the equations
(a) $\sqrt{3 \mathrm{x}+1}=\sqrt{2 \mathrm{x}-1}+1$;
(b) $2 \sqrt{x-1}=\sqrt{x+4}+1$.
Solve (a) The original equation is
$$
\sqrt{3 x+1}-\sqrt{2 x-1}=1 \text {. }
$$

Multiplying both sides by $\sqrt{3 x+1}+\sqrt{2 x-1}$ gives
$$
\begin{array}{l}
\sqrt{3 x+1}+\sqrt{2 x-1}=x+2 . \\
\text { (1) }+(2): 2 \sqrt{3 x+1}=x+3 . \\
\left\{\begin{array}{l}
x^{2}-6 x+5=0, \\
x>-\frac{1}{3} .
\end{array}\right.
\end{array}
$$

We get $x_{1}=1, x_{2}=5$, both of which are solutions to the original equation.
(b) The original equation is
$$
2 \sqrt{x-1}-\sqrt{x+4}=1 \text {. }
$$

Multiplying both sides by $2 \sqrt{x-1}+\sqrt{x+4}+4-4$ gives
$$
2 \sqrt{x-1}+\sqrt{x+4}=3 x-8 \text {. }
$$
(4) - (3) gives
$$
2 y'+4=3 x-9 \text {, }
$$

Simplifying, $(\sqrt{x+4})^{2}-2 \sqrt{x+4}-21=0$.
$$
(\sqrt{x+4}+7)(\sqrt{x+4}-3)=0 .
$$

We get $\sqrt{x+4}=3$.
So, $x=5$.
In this way, we have both a simple and quick method for creating radical equations and a unified method for solving them, achieving a relatively thorough solution to the problem of creating radical equations.
(Author's unit: Children's School of Yao County Cement Factory, Shaanxi Province)