Rút gọn biểu thức: P=x căn x-1/x-căn x - x căn x +1/x+ căn x + x+1/căn x

Đáp án:

 $P=\dfrac{(\sqrt{x}+1)^2}{\sqrt{x}}$

Giải thích các bước giải:

 Ta có:

$P=\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}$ với $x>0, x\neq 1$

$\Rightarrow P=\dfrac{(\sqrt{x})^3-1}{\sqrt{x}.(\sqrt{x}-1)}-\dfrac{(\sqrt{x})^3+1}{\sqrt{x}.(\sqrt{x}+1)}+\dfrac{x+1}{\sqrt{x}}$

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

$\Rightarrow  P=\dfrac{x+\sqrt{x}+1}{\sqrt{x}}-\dfrac{x-\sqrt{x}+1}{\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}$

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