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

(13 - \sqrt{101})^2 - (\sqrt{101} - 11)^2 = (13 - \sqrt{101} - (\sqrt{101} - 11))(13 - \sqrt{101} + (\sqrt{101} - 11)) = (13 - \sqrt{101} - \sqrt{101} + 11)(13 - \sqrt{101} + \sqrt{101} - 11) = (24 - 2\sqrt{101})(2) = 48 - 4\sqrt{101}

1. $$\frac{\sqrt{x} - 6}{\sqrt{x}} \cdot \frac{x - 36}{4x} = \frac{\sqrt{x} - 6}{\sqrt{x}} \cdot \frac{(\sqrt{x} - 6)(\sqrt{x} + 6)}{4x} = \frac{(\sqrt{x} - 6)^2(\sqrt{x} + 6)}{4x\sqrt{x}}$$
   Ответ: $$\frac{(\sqrt{x} - 6)^2(\sqrt{x} + 6)}{4x\sqrt{x}}$$
2. $$\left(\frac{\sqrt{a} - 5}{\sqrt{a} + 5} + \frac{20\sqrt{a}}{a - 25}\right) : \frac{\sqrt{a} + 5}{a - 5\sqrt{a}} = \left(\frac{\sqrt{a} - 5}{\sqrt{a} + 5} + \frac{20\sqrt{a}}{(\sqrt{a} - 5)(\sqrt{a} + 5)}\right) : \frac{\sqrt{a} + 5}{\sqrt{a}(\sqrt{a} - 5)} = \frac{(\sqrt{a} - 5)^2 + 20\sqrt{a}}{(\sqrt{a} + 5)(\sqrt{a} - 5)} : \frac{\sqrt{a} + 5}{\sqrt{a}(\sqrt{a} - 5)} = \frac{a - 10\sqrt{a} + 25 + 20\sqrt{a}}{(\sqrt{a} + 5)(\sqrt{a} - 5)} \cdot \frac{\sqrt{a}(\sqrt{a} - 5)}{\sqrt{a} + 5} = \frac{a + 10\sqrt{a} + 25}{(\sqrt{a} + 5)(\sqrt{a} - 5)} \cdot \frac{\sqrt{a}(\sqrt{a} - 5)}{\sqrt{a} + 5} = \frac{(\sqrt{a} + 5)^2}{(\sqrt{a} + 5)(\sqrt{a} - 5)} \cdot \frac{\sqrt{a}(\sqrt{a} - 5)}{\sqrt{a} + 5} = \frac{(\sqrt{a} + 5)^2\sqrt{a}(\sqrt{a} - 5)}{(\sqrt{a} + 5)^2(\sqrt{a} - 5)} = \sqrt{a}$$
   Ответ: $$\sqrt{a}$$