Hallo!
\(\displaystyle \frac{\sqrt{2}}{\sqrt{3}-\sqrt{5}} = \frac{\sqrt{2}\cdot\big(\sqrt{3}+\sqrt{5}\big)}{\big(\sqrt{3}-\sqrt{5}\big)\big(\sqrt{3}+\sqrt{5}\big)} = \frac{\sqrt{2}\cdot\big(\sqrt{3}+\sqrt{5}\big)}{3-5} = -\frac{\sqrt{6}+\sqrt{10}}{2}\).
Gruß.
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