Example 10 Simplify:
$$
\frac{(\sqrt{x}-\sqrt{y})^{3}+2 x \sqrt{x}+y \sqrt{y}}{x \sqrt{x}+y \sqrt{y}}+\frac{3 \sqrt{x y}-3 y}{x-y} .
$$
Let $\sqrt{x}=a+b, \sqrt{y}=a-b$. Then
$$
\sqrt{x y}=a^{2}-b^{2}, \sqrt{x}+\sqrt{y}=2 a, \sqrt{x}-\sqrt{y}=2 b \text {. }
$$

Therefore, the original expression is
$$
\begin{aligned}
= & \frac{(2 b)^{3}+2(a+b)^{3}+(a-b)^{3}}{(a+b)^{3}+(a-b)^{3}}+ \\
& \frac{3\left(a^{2}-b^{2}\right)-3(a-b)^{2}}{4 a b} \\
= & \frac{3\left(a^{2}+3 b^{2}\right)(a+b)}{2 a\left(a^{2}+3 b^{2}\right)}+\frac{3(a-b)}{2 a} \\
= & \frac{3 a+3 b+3 a-3 b}{2 a}=\frac{6 a}{2 a}=3 .
\end{aligned}
$$

[Note] This problem uses sum and difference substitution to transform the simplification of radicals into the simplification of fractions, thereby reducing the difficulty and improving the speed of solving the problem.
From the above examples, it can be seen that the essence of sum and difference substitution

is substitution and transformation, the key is to construct and set variables, the purpose is to introduce new variables to make complex calculations and proofs easier to handle.