4. Сократите дробь: a) c-2/c-√2 ; в) 7+√7/√7; б) x+√5/x²-5 ; г) a-y/√a+√y

a) $$ \frac{c-2}{c-\sqrt{2}} = \frac{(\sqrt{c}-\sqrt{2})(\sqrt{c}+\sqrt{2})}{c-\sqrt{2}} = \sqrt{c}+\sqrt{2}$$.

б) $$ \frac{7+\sqrt{7}}{\sqrt{7}} = \frac{\sqrt{7}(\sqrt{7}+1)}{\sqrt{7}} = \sqrt{7}+1$$.

в) $$ \frac{x+\sqrt{5}}{x^2-5} = \frac{x+\sqrt{5}}{(x-\sqrt{5})(x+\sqrt{5})} = \frac{1}{x-\sqrt{5}}$$.

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

Ответ: a) $$\sqrt{c}+\sqrt{2}$$; б) $$\sqrt{7}+1$$; в) $$\frac{1}{x-\sqrt{5}}$$; г) $$\sqrt{a}-\sqrt{y}$$