$\frac{a - b}{\sqrt{11b} - \sqrt{11a}} = \frac{(\sqrt{a})^2 - (\sqrt{b})^2}{\sqrt{11} * \sqrt{b} - \sqrt{11} * \sqrt{a}} = \frac{(\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b})}{\sqrt{11}(\sqrt{b} - \sqrt{a})} = -\frac{(\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b})}{\sqrt{11}(\sqrt{a} - \sqrt{b})} = -\frac{\sqrt{a} + \sqrt{b}}{\sqrt{11}}$

$\frac{2a + 10\sqrt{2ab} + 25b}{6a - 75b} = \frac{(\sqrt{2a})^2 + 10\sqrt{2ab} + (\sqrt{25b})^2}{3(2a - 25b)} = \frac{(\sqrt{2a})^2 + 2 * \sqrt{2a} * 5\sqrt{b} + (5\sqrt{b})^2}{3((\sqrt{2a})^2 - (\sqrt{25b})^2)} = \frac{(\sqrt{2a} + 5\sqrt{b})^2}{3((\sqrt{2a})^2 - (5\sqrt{b})^2)} = \frac{(\sqrt{2a} + 5\sqrt{b})^2}{3(\sqrt{2a} - 5\sqrt{b})(\sqrt{2a} + 5\sqrt{b})} = \frac{\sqrt{2a} + 5\sqrt{b}}{3(\sqrt{2a} - 5\sqrt{b})}$, если a > 0, b > 0

$\frac{a - 2\sqrt{a} + 4}{a\sqrt{a} + 8} = \frac{a - 2\sqrt{a} + 4}{\sqrt{a^2 * a} + 8} = \frac{a - 2\sqrt{a} + 4}{\sqrt{a^3} + 8} = \frac{a - 2\sqrt{a} + 4}{(\sqrt{a})^3 + 2^3} = \frac{a - 2\sqrt{a} + 4}{(\sqrt{a} + 2)((\sqrt{a})^2 - 2\sqrt{a} + 2^2)} = \frac{a - 2\sqrt{a} + 4}{(\sqrt{a} + 2)(a - 2\sqrt{a} + 4)} = \frac{1}{\sqrt{a} + 2}$