Cho biểu thức A = (x căn bậc hai x -1/ x - căn bậc hai x - x căn bậc hai x +1/ x + căn bậc hai x)

a) Điều kiện: $x>0,x\ne 1$.

$$\begin{gathered} A=\left(\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}\right):\frac{x-2\sqrt{x}+1}{x-1} \\ =\left[\frac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}-\frac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}\right]:\frac{{\left(\sqrt{x}-1\right)}^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)} \\ =\frac{x+\sqrt{x}+1-x+\sqrt{x}-1}{\sqrt{x}}.\frac{\sqrt{x}+1}{\sqrt{x}-1}=\frac{2\left(\sqrt{x}+1\right)}{\sqrt{x}-1} \end{gathered}$$

Vậy $A=\frac{2\left(\sqrt{x}+1\right)}{\sqrt{x}-1}$ với $x>0,x\ne 1$.