Сократите дробь: a) $$\frac{6+\sqrt{6}}{\sqrt{30}+\sqrt{5}}$$; б) $$\frac{9-a}{3+\sqrt{a}}$$.

а) $$\frac{6+\sqrt{6}}{\sqrt{30}+\sqrt{5}} = \frac{6+\sqrt{6}}{\sqrt{5}(\sqrt{6}+1)} = \frac{\sqrt{6}(\sqrt{6}+1)}{\sqrt{5}(\sqrt{6}+1)} = \frac{\sqrt{6}}{\sqrt{5}} = \frac{\sqrt{6}\sqrt{5}}{5} = \frac{\sqrt{30}}{5}$$. б) $$\frac{9-a}{3+\sqrt{a}} = \frac{(3-\sqrt{a})(3+\sqrt{a})}{3+\sqrt{a}} = 3-\sqrt{a}$$. <p><strong>Ответ:</strong></p> <ul> <li>а) $$\frac{\sqrt{30}}{5}$$</li> <li>б) $$3-\sqrt{a}$$</li> </ul>