Упр.406 ГДЗ Колмогоров 10-11 класс (Алгебра)

а) $$\frac{3}{\sqrt7-\sqrt5}=\frac{3(\sqrt7+\sqrt5)}{(\sqrt7-\sqrt5)(\sqrt7+\sqrt5)}=\frac{3(\sqrt7+\sqrt5)}{7-5}=\frac{3}{2}(\sqrt7+\sqrt5).$$

б) $$\frac{a-\sqrt2}{a+\sqrt2}=\frac{(a-\sqrt2)(a-\sqrt2)}{(a+\sqrt2)(a-\sqrt2)}=\frac{(a-\sqrt2)^2}{a^2-2}.$$

в) $$\frac{1}{\sqrt5+\sqrt2}=\frac{\sqrt5-\sqrt2}{(\sqrt5+\sqrt2)(\sqrt5-\sqrt2)}=\frac{\sqrt5-\sqrt2}{5-2}=\frac{\sqrt5-\sqrt2}{3}.$$

г) $$\frac{\sqrt6+1}{\sqrt6-1}=\frac{(\sqrt6+1)(\sqrt6+1)}{(\sqrt6-1)(\sqrt6+1)}=\frac{(\sqrt6+1)^2}{6-1}=\frac{6+2\sqrt6+1}{5}=\frac{7+2\sqrt6}{5}.$$