Rút gọn: F = (2 + căn bậc hai của x/x + 2 căn bậc hai của x + 1

* Hướng dẫn giải

$\begin{array}{l}F=\left(\frac{2+\sqrt{x}}{x+2\sqrt{x}+1}-\frac{\sqrt{x}-2}{x-1}\right)\left(\frac{x\sqrt{x}+x-\sqrt{x}-1}{\sqrt{x}}\right)\\ =\left[\frac{2+\sqrt{x}}{{\left(\sqrt{x}+1\right)}^2}-\frac{\sqrt{x}-2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right].\frac{x\left(\sqrt{x}+1\right)-\left(\sqrt{x}+1\right)}{\sqrt{x}}\\ =\frac{\left(2+\sqrt{x}\right)\left(\sqrt{x}-1\right)-\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}{{\left(\sqrt{x}+1\right)}^2\left(\sqrt{x}-1\right)}.\frac{{\left(\sqrt{x}+1\right)}^2\left(\sqrt{x}-1\right)}{\sqrt{x}}\\ =\frac{x+\sqrt{x}-2-x+\sqrt{x}+2}{\sqrt{x}}=\frac{2\sqrt{x}}{\sqrt{x}}=2\end{array}$