Đáp án+Giải thích các bước giải:
ĐKXĐ : `x ≥ 0 ; x \ne 1`
`P = \frac{x - \sqrt{x}}{x + \sqrt{x} + 1} - \frac{2x+ \sqrt{x}}{\sqrt{x}} + \frac{2(x - 1)}{\sqrt{x} - 1}`
`= \frac{x - \sqrt{x}}{x + \sqrt{x} + 1} - \frac{\sqrt{x}(2\sqrt{x} + 1)}{\sqrt{x}} + \frac{2(x - 1)}{\sqrt{x} - 1}`
`= \frac{x - \sqrt{x}}{x + \sqrt{x} + 1} - (2\sqrt{x} + 1)+ \frac{2(x - 1)}{\sqrt{x} - 1}`
`= \frac{(x - \sqrt{x})(\sqrt{x} - 1) - (2\sqrt{x} + 1)(x\sqrt{x} - 1) + 2(x - 1)(x + \sqrt{x} + 1)}{(\sqrt{x} - 1)(x + \sqrt{x} + 1)}`
`= \frac{2x\sqrt{x} - 2x + \sqrt{x} - 1}{(\sqrt{x} - 1)(x + \sqrt{x} + 1)}`
`= \frac{2x(\sqrt{x} - 1) + (\sqrt{x} - 1)}{(\sqrt{x} - 1)(x + \sqrt{x} + 1)}`
`= \frac{(\sqrt{x} - 1)(2x + 1)}{(\sqrt{x} - 1)(x + \sqrt{x} + 1)}`
`= \frac{2x + 1}{x + \sqrt{x} + 1}`
