Упростите выражения: б) $$rac{1}{1-\sqrt{2}}$$; г) $$rac{a}{\sqrt{a}+\sqrt{b}}$$; е) $$rac{15}{2\sqrt{5}+5}$$.

б) $$rac{1}{1-\sqrt{2}} = \frac{1}{1-\sqrt{2}} \cdot \frac{1+\sqrt{2}}{1+\sqrt{2}} = \frac{1+\sqrt{2}}{1-2} = \frac{1+\sqrt{2}}{-1} = -1-\sqrt{2}$$.

Ответ: $$-1-\sqrt{2}$$

г) $$rac{a}{\sqrt{a}+\sqrt{b}} = \frac{a(\sqrt{a}-\sqrt{b})}{(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})} = \frac{a(\sqrt{a}-\sqrt{b})}{a-b}$$.

Ответ: $$\frac{a(\sqrt{a}-\sqrt{b})}{a-b}$$

е) $$rac{15}{2\sqrt{5}+5} = \frac{15(2\sqrt{5}-5)}{(2\sqrt{5}+5)(2\sqrt{5}-5)} = \frac{15(2\sqrt{5}-5)}{4\cdot 5 - 25} = \frac{15(2\sqrt{5}-5)}{20 - 25} = \frac{15(2\sqrt{5}-5)}{-5} = -3(2\sqrt{5}-5) = -6\sqrt{5}+15 = 15-6\sqrt{5}$$.

Ответ: $$15-6\sqrt{5}$$