5. Сократите дробь: а) \(\frac{\sqrt{10}+5}{2+\sqrt{10}}\) ; б) \(\frac{x-3\sqrt{x}}{2\sqrt{x}-6}\)

a) Сократим дробь \(\frac{\sqrt{10}+5}{2+\sqrt{10}}\)

1. \(\frac{\sqrt{10}+5}{2+\sqrt{10}} = \frac{\sqrt{10}+5}{2+\sqrt{10}} = \frac{\sqrt{5}(\sqrt{2}+\sqrt{5})}{\sqrt{2}(\sqrt{2}+\sqrt{5})} = \frac{\sqrt{5}}{\sqrt{2}} = \frac{\sqrt{10}}{2}\)

б) Сократим дробь \(\frac{x-3\sqrt{x}}{2\sqrt{x}-6}\)

1. \(\frac{x-3\sqrt{x}}{2\sqrt{x}-6} = \frac{\sqrt{x}(\sqrt{x}-3)}{2(\sqrt{x}-3)} = \frac{\sqrt{x}}{2}\)

Ответ: a) \(\frac{\sqrt{10}}{2}\); б) \(\frac{\sqrt{x}}{2}\)