A= (√x/ √x-1-1/ x-√x) : (1/ 1+x+2/ x-1) -Rút gọn bt A

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1. Giải thích các bước giải:
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   \begin{array}{l}
   A = (\frac{{\sqrt x }}{{\sqrt x – 1}} – \frac{1}{{x – \sqrt x }}):(\frac{1}{{1 + x}} + \frac{2}{{x – 1}})\\
   A = {\rm{[}}\frac{{\sqrt x }}{{\sqrt x – 1}} – \frac{1}{{\sqrt x .(\sqrt x – 1)}}{\rm{]: [}}\frac{{x – 1 + 2.(x + 1)}}{{(1 + x).(x – 1)}}{\rm{]}}\\
   {\rm{A = }}\frac{{x – 1}}{{\sqrt x .(\sqrt x – 1)}}:\frac{{3x + 1}}{{(1 + x).(x – 1)}}\\
   A = \frac{{(\sqrt x – 1).(\sqrt x + 1)}}{{\sqrt x .(\sqrt x – 1)}}.\frac{{(1 + x).(x – 1)}}{{3x + 1}}\\
   A = \frac{{\sqrt x + 1}}{{\sqrt x }}.\frac{{(1 + x).(x – 1)}}{{3x + 1}}
   \end{array}$

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