rút gọn P=4/căn x-1 +3/căn x-1 -6 căn x+2 (x>0,x khác 1) R=(1/ căn x-1 -căn x/x-1):1/căn x+1 (x>0 x khác 1)

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1. $P=\dfrac{4}{\sqrt{x}-1}+\dfrac{3}{\sqrt{x}-1}-\dfrac{6}{\sqrt{x}+2}$     ĐK: $x>0;x\neq1$

   $P=\dfrac{7}{\sqrt{x}-1}-\dfrac{6}{\sqrt{x}+2}$

   $P=\dfrac{7(\sqrt{x}+2)-6(\sqrt{x}-1)}{(\sqrt{x}-1)(\sqrt{x}+2)}$

   $P=\dfrac{7\sqrt{x}+14-6\sqrt{x}+6}{(\sqrt{x}-1)(\sqrt{x}+2)}$

   $P=\dfrac{\sqrt{x}+20}{(\sqrt{x}-1)(\sqrt{x}+2)}$

   Vậy $P=\dfrac{\sqrt{x}+20}{(\sqrt{x}-1)(\sqrt{x}+2)}$

   $R=(\dfrac{1}{\sqrt{x}-1}-\dfrac{\sqrt{x}}{x-1}):\dfrac{1}{\sqrt{x}+1}$     ĐK: $x>0;x\neq1$

   $R=(\dfrac{1}{\sqrt{x}-1}-\dfrac{\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}).(\sqrt{x}+1)$

   $R=\dfrac{\sqrt{x}+1-\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}.(\sqrt{x}+1)$

   $R=\dfrac{1}{\sqrt{x}-1}$

   Vậy $R=\dfrac{1}{\sqrt{x}-1}$ với $x>0;x\neq1$

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2. P= 4/√x-1 + 3/√x-1 – 6/√x+2

   =4.(√x+2)/(√x-1).(√x+2) + 3.(√x+2)/(√x-1).(√x+2) – 6.(√x-1)/(√x-1).(√x+2)

   = 4√x +8 + 3√x +6 – 6√x + 6 / (√x-1).(√x+2)

   = √x + 20 / (√x-1).(√x+2)

   R=( 1/√x-1 – √x / x-1 ) : 1/√x +1

   = ( √x +1/ (√x-1).(√x+1) – √x / (√x+1).(√x-1) ) : 1 /√x+1

   = (√x +1-√x / (√x-1).(√x+1) ) : 1/√x +1

   =   1/(√x-1).(√x+1) . (√x+1) /1

   =1/√x -1 

    

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