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

$$(\sqrt{13} - \sqrt{101})^2 - (\sqrt{101} - 11)^2 = (13 - 2\sqrt{13}\sqrt{101} + 101) - (101 - 22\sqrt{101} + 121) = 114 - 2\sqrt{1313} - 222 + 22\sqrt{101} = -108 - 2\sqrt{1313} + 22\sqrt{101}$$

Ответ: $$-108 - 2\sqrt{1313} + 22\sqrt{101}$$

$$\frac{\sqrt{x} - 6}{\sqrt{x}} \cdot \frac{x - 36}{4x} = \frac{(\sqrt{x} - 6)(x - 36)}{\sqrt{x} \cdot 4x} = \frac{(\sqrt{x} - 6)(\sqrt{x} - 6)(\sqrt{x} + 6)}{\sqrt{x} \cdot 4x} = \frac{(\sqrt{x} - 6)^2(\sqrt{x} + 6)}{4x\sqrt{x}}$$

Ответ:$$\frac{(\sqrt{x} - 6)^2(\sqrt{x} + 6)}{4x\sqrt{x}}$$.

$$\left(\frac{\sqrt{a} - 5}{\sqrt{a} + 5} + \frac{20\sqrt{a}}{a - 25}\right) : \frac{\sqrt{a} + 5}{a - 5\sqrt{a}} = \left(\frac{\sqrt{a} - 5}{\sqrt{a} + 5} + \frac{20\sqrt{a}}{(\sqrt{a} - 5)(\sqrt{a} + 5)}\right) : \frac{\sqrt{a} + 5}{a - 5\sqrt{a}} = \frac{(\sqrt{a} - 5)^2 + 20\sqrt{a}}{(\sqrt{a} + 5)(\sqrt{a} - 5)} : \frac{\sqrt{a} + 5}{a - 5\sqrt{a}} = \frac{a - 10\sqrt{a} + 25 + 20\sqrt{a}}{(\sqrt{a} + 5)(\sqrt{a} - 5)} : \frac{\sqrt{a} + 5}{\sqrt{a}(\sqrt{a} - 5)} = \frac{a + 10\sqrt{a} + 25}{(\sqrt{a} + 5)(\sqrt{a} - 5)} : \frac{\sqrt{a} + 5}{\sqrt{a}(\sqrt{a} - 5)} = \frac{(\sqrt{a} + 5)^2}{(\sqrt{a} + 5)(\sqrt{a} - 5)} \cdot \frac{\sqrt{a}(\sqrt{a} - 5)}{\sqrt{a} + 5} = \frac{(\sqrt{a} + 5)^2 \sqrt{a}(\sqrt{a} - 5)}{(\sqrt{a} + 5)(\sqrt{a} - 5)(\sqrt{a} + 5)} = \frac{\sqrt{a}(\sqrt{a} + 5)}{\sqrt{a} + 5} = \sqrt{a}$$

Ответ:$$\sqrt{a}$$.