Rút gọn biểu thức ​\(P=\left(\frac{2 x+1}{\sqrt{x^{3}}-1}-\frac{1}{\sqrt{x}-1}\right):\left(1-\frac{x+4}{x+\sqrt{x}+1}\right)\) ta được:

* Hướng dẫn giải

 \(\begin{array}{l} ĐK:\left\{ {\begin{array}{*{20}{l}} {x \ge 0}\\ {x \ne 1} \end{array}} \right.\\ P = \left( {\frac{{2x + 1}}{{\sqrt {{x^3}} - 1}} - \frac{1}{{\sqrt x - 1}}} \right):\left( {1 - \frac{{x + 4}}{{x + \sqrt x + 1}}} \right)\\ = \left( {\frac{{2x + 1}}{{(\sqrt x - 1)(x + \sqrt x + 1)}} - \frac{1}{{\sqrt x - 1}}} \right):\left( {\frac{{x + \sqrt x + 1 - x - 4}}{{x + \sqrt x + 1}}} \right)\\ = \frac{{2x + 1 - x - \sqrt x - 1}}{{(\sqrt x - 1)(x + \sqrt x + 1)}}:\frac{{\sqrt x - 3}}{{x + \sqrt x + 1}} = \frac{{x - \sqrt x }}{{(\sqrt x - 1)(x + \sqrt x + 1)}} \cdot \frac{{x + \sqrt x + 1}}{{\sqrt x - 3}}(x \ne 9)\\ = \frac{{\sqrt x (\sqrt x - 1)}}{{(\sqrt x - 1)(\sqrt x - 3)}} = \frac{{\sqrt x }}{{\sqrt x - 3}} \end{array}\)