Задание 7. Сократите дробь. a) $$rac{2-\sqrt{2}}{\sqrt{3}-\sqrt{6}}$$ b) $$rac{\sqrt{14}+2}{7+\sqrt{14}}$$

a) $$\frac{2-\sqrt{2}}{\sqrt{3}-\sqrt{6}} = \frac{2-\sqrt{2}}{\sqrt{3}(1-\sqrt{2})} = \frac{\sqrt{2}(\sqrt{2}-1)}{\sqrt{3}(1-\sqrt{2})} = -\frac{\sqrt{2}}{\sqrt{3}} = -\frac{\sqrt{6}}{3}$$

б) $$\frac{\sqrt{14}+2}{7+\sqrt{14}} = \frac{\sqrt{2}\sqrt{7}+2}{7+\sqrt{14}} = \frac{\sqrt{2}(\sqrt{7}+\sqrt{2}\sqrt{2})}{\sqrt{7}\sqrt{7}+\sqrt{14}} = \frac{\sqrt{2}(\sqrt{7}+\sqrt{4})}{\sqrt{7}^2 + \sqrt{2}\sqrt{7}} = \frac{\sqrt{2}(\sqrt{7}+2)}{\sqrt{7}(\sqrt{7}+ \sqrt{2})} = \frac{\sqrt{2}(\sqrt{7}+2)}{\sqrt{7}(\sqrt{7}+ \sqrt{2})}$$