9. Упростите выражение (13-101)2 - √(√101-11)2. 3) √x-6x-36 √x4x 4) √a-5, 20√a); √a+5. a-25a-5√a √a +5 + :

$$(13-\sqrt{101})^2 - \sqrt{(\sqrt{101}-11)^2} = (13-\sqrt{101})^2 - |\sqrt{101} - 11| = (13-\sqrt{101})^2 - (\sqrt{101} - 11) = 169 - 26\sqrt{101} + 101 - \sqrt{101} + 11 = 281 - 27\sqrt{101}$$
3) $$\frac{\sqrt{x} - 6}{\sqrt{x}} : \frac{x - 36}{4x} = \frac{\sqrt{x} - 6}{\sqrt{x}} \cdot \frac{4x}{x - 36} = \frac{\sqrt{x} - 6}{\sqrt{x}} \cdot \frac{4x}{(\sqrt{x} - 6)(\sqrt{x} + 6)} = \frac{4x}{\sqrt{x}(\sqrt{x} + 6)} = \frac{4\sqrt{x}}{\sqrt{x} + 6}$$
4) $$\frac{\sqrt{a}-5}{\sqrt{a}+5} + \frac{20\sqrt{a}}{a-25} : \frac{\sqrt{a}+5}{a-5\sqrt{a}} = \frac{\sqrt{a}-5}{\sqrt{a}+5} + \frac{20\sqrt{a}}{(\sqrt{a}-5)(\sqrt{a}+5)} \cdot \frac{\sqrt{a}(\sqrt{a}-5)}{\sqrt{a}+5} = \frac{\sqrt{a}-5}{\sqrt{a}+5} + \frac{20\sqrt{a} \cdot \sqrt{a}}{(\sqrt{a}+5)^2} = \frac{(\sqrt{a}-5)(\sqrt{a}+5)}{(\sqrt{a}+5)^2} + \frac{20a}{(\sqrt{a}+5)^2} = \frac{a-25+20a}{(\sqrt{a}+5)^2} = \frac{21a-25}{(\sqrt{a}+5)^2}$$