Rút gọn biểu thức: A=left(frac2 sqrtx+xx

$A=\left(\frac{2 \sqrt{x}+x}{x \sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\right):\left(1-\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)$ với $x \geq 0, x \neq 1$

$=\left(\frac{2 \sqrt{x}+x}{(\sqrt{x})^{3}-1}-\frac{1}{\sqrt{x}-1}\right): \frac{x+\sqrt{x}+1-(\sqrt{x}+2)}{x+\sqrt{x}+1}$

$=\left(\frac{2 \sqrt{x}+x}{(\sqrt{x}-1) \cdot(x+\sqrt{x}+1)}-\frac{x+\sqrt{x}+1}{(\sqrt{x}-1) \cdot(x+\sqrt{x}+1)}\right): \frac{x+\sqrt{x}+1-(\sqrt{x}+2)}{x+\sqrt{x}+1}$

$=\frac{2 \sqrt{x}+x-x-\sqrt{x}-1}{(\sqrt{x}-1)(x+\sqrt{x}+1)}: \frac{x-1}{x+\sqrt{x}+1}$

$=\frac{\sqrt{x}-1}{(\sqrt{x}-1)(x+\sqrt{x}+1)} \cdot \frac{x+\sqrt{x}+1}{x-1}$

$=\frac{(\sqrt{x}-1) \cdot(x+\sqrt{x}+1)}{(\sqrt{x}-1)(x+\sqrt{x}+1) \cdot(x-1)}$

$=\frac{1}{x-1}$