\(S = \left( {\frac{{\sqrt x  + 3}}{{\sqrt x  - 2}...

B

- Hướng dẫn giải

Phương pháp giải:

Giải chi tiết:

\(\begin{array}{l}4)\,\,S = \left( {\frac{{\sqrt x  + 3}}{{\sqrt x  - 2}} + \frac{{\sqrt x  + 2}}{{3 - \sqrt x }} + \frac{{\sqrt x  + 2}}{{x - 5\sqrt x  + 6}}} \right):\left( {1 - \frac{{\sqrt x }}{{\sqrt x  + 1}}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {DK:\,\,x \ge 0,\,\,x \ne 4,\,\,x \ne 9} \right)\\\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{\sqrt x  + 3}}{{\sqrt x  - 2}} - \frac{{\sqrt x  + 2}}{{\sqrt x  - 3}} + \frac{{\sqrt x  + 2}}{{(\sqrt x  - 3).(\sqrt x  - 2)}}} \right):\left( {\frac{{\sqrt x  + 1 - \sqrt x }}{{\sqrt x  + 1}}} \right)\\\,\,\,\,\,\,\,\,\,\, = \frac{{(\sqrt x  + 3)(\sqrt x  - 3) - (\sqrt x  + 2)(\sqrt x  - 2) + \sqrt x  + 2}}{{(\sqrt x  - 3).(\sqrt x  - 2)}}:\frac{1}{{\sqrt x  + 1}}\\\,\,\,\,\,\,\,\,\,\, = \frac{{x - 9 - (x - 4) + \sqrt x  + 2}}{{(\sqrt x  - 3).(\sqrt x  - 2)}}:\frac{1}{{\sqrt x  + 1}}\\\,\,\,\,\,\,\,\,\, = \frac{{x - 9 - x + 4 + \sqrt x  + 2}}{{(\sqrt x  - 3).(\sqrt x  - 2)}}:\frac{1}{{\sqrt x  + 1}}\\\,\,\,\,\,\,\,\, = \frac{{\sqrt x  - 3}}{{(\sqrt x  - 3).(\sqrt x  - 2)}}.(\sqrt x  + 1)\\\,\,\,\,\,\,\,\, = \frac{{\sqrt x  + 1}}{{\sqrt x  - 2}}.\end{array}\)