30. Rationalize the fraction $\frac{1}{\sqrt{2}+\sqrt{3}-\sqrt{5}}$.
Solution.

$$
\begin{aligned}
\frac{1}{\sqrt{2}+\sqrt{3}-\sqrt{5}} & =\frac{1}{\sqrt{2}+\sqrt{3}-\sqrt{5}} \cdot \frac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{\sqrt{2}+\sqrt{3}+\sqrt{5}} \\
& =\frac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{(\sqrt{2}+\sqrt{3})^{2}-5}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{2 \sqrt{6}} \\
& =\frac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{2 \sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}} \\
& =\frac{\sqrt{6}(\sqrt{2}+\sqrt{3}+\sqrt{5})}{12}
\end{aligned}
$$

(full solution 8 points)

(partial solution up to (*) 4 points)

(the denominator can be grouped in other ways)