by \(T = \frac{{\sqrt x + 1}}{{x – 1}} – \frac{{x + 2}}{{x\sqrt x – 1}} – \frac{{\sqrt x + 1}}{{x + \sqrt x + 1}}\)
A \(T= \frac{{ – \sqrt x }}{{x + \sqrt x + 1}}\)
B \(T= \frac{{ – \sqrt x }}{{x – \sqrt x + 1}}\)
C \(T= \frac{{ \sqrt x }}{{x + \sqrt x + 1}}\)
D \(T= \frac{{ -2 \sqrt x }}{{x + \sqrt x + 1}}\)
Hướng dẫn Chọn đáp án là: A
Lời giải chi tiết:
\(\begin{array}{l}\,\,\,T = \frac{{\sqrt x + 1}}{{x – 1}} – \frac{{x + 2}}{{x\sqrt x – 1}} – \frac{{\sqrt x + 1}}{{x + \sqrt x + 1}}\,\,\,\,\,\left( {DK:\,\,x \ge 0,\,\,x \ne 1} \right)\\\,\,\,\,\,\,\,\,\,\,\, = \frac{{\sqrt x + 1}}{{(\sqrt x – 1)(\sqrt x + 1)}} – \frac{{x + 2}}{{(\sqrt x – 1)(x + \sqrt x + 1)}} – \frac{{\sqrt x + 1}}{{x + \sqrt x + 1}}\\\,\,\,\,\,\,\,\,\,\, = \frac{1}{{\sqrt x – 1}} – \frac{{x + 2}}{{(\sqrt x – 1)(x + \sqrt x + 1)}} – \frac{{\sqrt x + 1}}{{x + \sqrt x + 1}}\\\,\,\,\,\,\,\,\,\,\, = \frac{{x + \sqrt x + 1 – (x + 2) – (\sqrt x + 1)(\sqrt x – 1)}}{{(\sqrt x – 1)(x + \sqrt x + 1)}}\\\,\,\,\,\,\,\,\,\,\, = \frac{{x + \sqrt x + 1 – x – 2 – (x – 1)}}{{(\sqrt x – 1)(x + \sqrt x + 1)}}\\\,\,\,\,\,\,\,\,\, = \frac{{\sqrt x – 1 – x + 1}}{{(\sqrt x – 1)(x + \sqrt x + 1)}}\\\,\,\,\,\,\,\,\, = \frac{{\sqrt x – x}}{{(\sqrt x – 1)(x + \sqrt x + 1)}}\\\,\,\,\,\,\,\,\, = \frac{{ – \sqrt x \left( {\sqrt x – 1} \right)}}{{(\sqrt x – 1)(x + \sqrt x + 1)}}\\\,\,\,\,\,\,\,\, = \frac{{ – \sqrt x }}{{x + \sqrt x + 1}}.\end{array}\)
