3. Сократите дробь: a) 3-b²/√3+b б) 5-√5/√10-√2 в) 4x²+4x√a+a/2x+√a

Ответ:

1. a) $$\frac{3-b^2}{\sqrt{3} + b} = \frac{(\sqrt{3} - b)(\sqrt{3} + b)}{\sqrt{3} + b} = \sqrt{3} - b$$
2. б) $$\frac{5 - \sqrt{5}}{\sqrt{10} - \sqrt{2}} = \frac{\sqrt{5}(\sqrt{5} - 1)}{\sqrt{2}(\sqrt{5} - 1)} = \frac{\sqrt{5}}{\sqrt{2}} = \frac{\sqrt{5} \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{\sqrt{10}}{2}$$
3. в) $$\frac{4x^2 + 4x\sqrt{a} + a}{2x + \sqrt{a}} = \frac{(2x)^2 + 2 \cdot 2x \cdot \sqrt{a} + (\sqrt{a})^2}{2x + \sqrt{a}} = \frac{(2x + \sqrt{a})^2}{2x + \sqrt{a}} = 2x + \sqrt{a}$$