Toán Lớp 9: P=((x√x)/(x√x-1)+√x/(1-√x))÷(√x+1)/(x+√x+1)
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Toán Lớp 9: P=((x√x)/(x√x-1)+√x/(1-√x))÷(√x+1)/(x+√x+1)
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P = \left( {\dfrac{{x\sqrt x }}{{x\sqrt x – 1}} + \dfrac{{\sqrt x }}{{1 – \sqrt x }}} \right):\dfrac{{\sqrt x + 1}}{{x + \sqrt x + 1}}\\
= \dfrac{{x\sqrt x – \sqrt x \left( {x + \sqrt x + 1} \right)}}{{\left( {\sqrt x – 1} \right)\left( {x + \sqrt x + 1} \right)}}.\dfrac{{x + \sqrt x + 1}}{{\sqrt x + 1}}\\
= \dfrac{{x\sqrt x – x\sqrt x – x – \sqrt x }}{{\sqrt x – 1}}.\dfrac{1}{{\sqrt x + 1}}\\
= \dfrac{{ – \sqrt x \left( {\sqrt x + 1} \right)}}{{\sqrt x – 1}}.\dfrac{1}{{\sqrt x + 1}}\\
= \dfrac{{ – \sqrt x }}{{\sqrt x – 1}}\\
= \dfrac{{\sqrt x }}{{1 – \sqrt x }}
\end{array}$