Cho biểu thức B=left(fracsqrtx-2x-1-fracsqrtx+2x+2 sqrtx+1right) cdot

Ta có $B=\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2 \sqrt{x}+1}\right) \cdot \frac{(1-x)^{2}}{2}$

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

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

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

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

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

Vậy $B=\sqrt{x}-x$