Rút gọn biều thức: B=frac4sqrtx+1+frac21-sqrtx-fracsqrtx-5x-1 với x geq 0, x neq

Với $x \geq 0$ và $x \neq 1,$ ta có:

$B=\frac{4}{\sqrt{x}+1}+\frac{2}{1-\sqrt{x}}-\frac{\sqrt{x}-5}{x-1}$

$=\frac{4}{\sqrt{x}+1}-\frac{2}{\sqrt{x}-1}-\frac{\sqrt{x}-5}{(\sqrt{x})^{2}-1}$

$=\frac{4(\sqrt{x}-1)}{(\sqrt{x}+1)(\sqrt{x}-1)}-\frac{2(\sqrt{x}+1)}{(\sqrt{x}+1)(\sqrt{x}-1)}-\frac{\sqrt{x}-5}{(\sqrt{x}+1)(\sqrt{x}-1)}$

$=\frac{4(\sqrt{x}-1)-2(\sqrt{x}+1)-(\sqrt{x}-5)}{(\sqrt{x}+1)(\sqrt{x}-1)}$

$=\frac{4 \sqrt{x}-4-2 \sqrt{x}-2-\sqrt{x}+5}{(\sqrt{x}+1)(\sqrt{x}-1)}$

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

Vậy $B =\frac{1}{\sqrt{x}+1}$