Задание 8. Сократите дробь и избавьтесь от иррациональности в знаменателе. a) $$rac{7}{1+\sqrt{5}}$$ b) $$\frac{\sqrt{5}}{\sqrt{5}+\sqrt{2}}$$

a) $$\frac{7}{1+\sqrt{5}} = \frac{7(1-\sqrt{5})}{(1+\sqrt{5})(1-\sqrt{5})} = \frac{7(1-\sqrt{5})}{1-5} = \frac{7(1-\sqrt{5})}{-4} = -\frac{7}{4} (1-\sqrt{5})$$

б) $$\frac{\sqrt{5}}{\sqrt{5}+\sqrt{2}} = \frac{\sqrt{5}(\sqrt{5}-\sqrt{2})}{(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})} = \frac{5-\sqrt{10}}{5-2} = \frac{5-\sqrt{10}}{3}$$