1. Упростите выражение: а) $$\frac{5a+10}{b-7} : \frac{a^2+4a+4}{2b-14}$$; б) $$\frac{\sqrt{50}-\sqrt{6}}{\sqrt{12}}$$

Решение:

1. \(\text{а) } \frac{5a+10}{b-7} : \frac{a^2+4a+4}{2b-14} = \frac{5(a+2)}{b-7} \cdot \frac{2(b-7)}{(a+2)^2} = \frac{5 \cdot 2(b-7)(a+2)}{(b-7)(a+2)^2} = \frac{10}{a+2}\)
2. \(\text{б) } \frac{\sqrt{50}-\sqrt{6}}{\sqrt{12}} = \frac{\sqrt{25 \cdot 2}-\sqrt{6}}{\sqrt{4 \cdot 3}} = \frac{5\sqrt{2}-\sqrt{6}}{2\sqrt{3}} = \frac{(5\sqrt{2}-\sqrt{6})\sqrt{3}}{(2\sqrt{3})\sqrt{3}} = \frac{5\sqrt{6}-\sqrt{18}}{6} = \frac{5\sqrt{6}-3\sqrt{2}}{6}\)

Ответ: а) $$\frac{10}{a+2}$$; б) $$\frac{5\sqrt{6}-3\sqrt{2}}{6}$$.