Rút gọn P=A:B A= $\frac{x-1}{căn x-1}$ – $\frac{(x.căn x) +1}{x-1}$ B= $\frac{x}{căn x-1}$

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1. $A=\dfrac{x-1}{\sqrt[]{x}-1}-\dfrac{x\sqrt[]{x}+1}{x-1}$

   $=\dfrac{(\sqrt[]{x}-1)(\sqrt[]{x}+1)}{\sqrt[]{x}-1}-\dfrac{(\sqrt[]{x}+1)(x-\sqrt[]{x}+1)}{(\sqrt[]{x}-1)(\sqrt[]{x}+1)}$

   $=\sqrt[]{x}+1-\dfrac{x-\sqrt[]{x}+1}{\sqrt[]{x}-1}$

   $=\dfrac{(\sqrt[]{x}+1)(\sqrt[]{x}-1)-x+\sqrt[]{x}-1}{\sqrt[]{x}-1}$

   $=\dfrac{x-1-x+\sqrt[]{x}-1}{\sqrt[]{x}-1}$

   $=\dfrac{\sqrt[]{x}-2}{\sqrt[]{x}-1}$

   $P=A:B$

   $=\dfrac{\sqrt[]{x}-2}{\sqrt[]{x}-1}.\dfrac{\sqrt[]{x}-1}{x}$

   $=\dfrac{\sqrt[]{x}-2}{x}$ ($x>0$)

    

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