Question

Rút gọn biểu thức 

A = ( 1/ x + \(\sqrt{x}\)- 1/ \(\sqrt{x}\)+1) : \(\sqrt{x}\)-1/x+2\(\sqrt{x}\)+1

Answer 1

\(đkx\ge0\\ A=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}+1\right)}-\dfrac{1}{\sqrt{x}+1}\right):\left(\dfrac{\sqrt{x}-1}{\left(\sqrt{x}+1\right)^2}\right)\\ =\dfrac{1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}.\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}-1}\\ =\dfrac{-\left(\sqrt{x}-1\right)}{\sqrt{x}}.\dfrac{\sqrt{x}+1}{\sqrt{x}-1}=\dfrac{-\sqrt{x}-1}{\sqrt{x}}\)

Answer 2

Với `x >= 0,x \ne 1` có:

`A=(1/[x+\sqrt{x}]-1/[\sqrt{x}+1]):[\sqrt{x}-1]/[x+2\sqrt{x}+1]`

`A=[1-\sqrt{x}]/[\sqrt{x}(\sqrt{x}+1)].[(\sqrt{x}+1)^2]/[\sqrt{x}-1]`

`A=[-(\sqrt{x}-1)(\sqrt{x}+1)]/[\sqrt{x}(\sqrt{x}-1)]`

`A=[-\sqrt{x}-1]/\sqrt{x}`