Câu 7 b = 2x + 1 + x + 5x - x - 2 chia 1 trừ 3 phần 4 - x

Đáp án + Giải thích các bước giải:

$P =\bigg(\dfrac{2}{\sqrt{x} + 1} + \dfrac{x + 5}{x - \sqrt{x} - 2}\bigg) : \bigg(1 - \dfrac{3}{4 - x}\bigg)(x \ge 0, x \ne 4)$

$= \bigg(\dfrac{2}{\sqrt{x} + 1} + \dfrac{x + 5}{(\sqrt{x} + 1)(\sqrt{x} - 2)}\bigg) : \dfrac{4 - x - 3}{4 - x}$

$= \dfrac{2(\sqrt{x} - 2) + x + 5}{(\sqrt{x} + 1)(\sqrt{x} - 2)} : \dfrac{1 - x}{4 - x}$

$= \dfrac{2\sqrt{x} - 4 + x + 5}{(\sqrt{x} +1)(\sqrt{x} - 2)} . \dfrac{4 - x}{1 - x}$

$= \dfrac{x + 2\sqrt{x} + 1}{(\sqrt{x} + 1)(\sqrt{x} - 2)} . \dfrac{(\sqrt{x} + 2)(2- \sqrt{x})}{(\sqrt{x} + 1)(1 - \sqrt{x})}$

$= \dfrac{(\sqrt{x} + 1)^2}{(\sqrt{x} +1)(\sqrt{x} - 2)} . \dfrac{(\sqrt{x} +2)(\sqrt{x} -2)}{(\sqrt{x} + 1)(\sqrt{x} - 1)}$

$= \dfrac{(\sqrt{x} + 1)^2(\sqrt{x} + 2)(\sqrt{x} - 2)}{(\sqrt{x} + 1)^2(\sqrt{x} - 1)(\sqrt{x} - 2)}$

$= \dfrac{\sqrt{x} + 2}{\sqrt{x} - 1}$