6. Сократите дробь: a) 5-V5 V10-12 6) 6-4 16-2

6. Сократите дробь:

a) $$\frac{5-\sqrt{5}}{\sqrt{10}-\sqrt{2}} = \frac{\sqrt{5}(\sqrt{5}-1)}{\sqrt{2}(\sqrt{5}-1)} = \frac{\sqrt{5}}{\sqrt{2}} = \frac{\sqrt{5}\cdot\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}} = \frac{\sqrt{10}}{2} $$.

б) $$\frac{b-4}{\sqrt{b}-2} = \frac{(\sqrt{b}-2)(\sqrt{b}+2)}{\sqrt{b}-2} = \sqrt{b}+2 $$.

Ответ: a) $$\frac{\sqrt{10}}{2}$$; б) $$\sqrt{b}+2$$