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

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

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

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

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: а) $$ \frac{(c-2) \cdot \sqrt{2}}{2} $$, б) $$ \frac{1}{x-\sqrt{5}} $$, в) $$ \sqrt{7}+1 $$, г) $$ \sqrt{a}-\sqrt{y} $$.