Cho biểu thức : 9 xcăn x-1/ x- căn x- x căn x+1/ x+ căn x : 2( x-2cănx+1)/ x-1 a) Rút gọn A b) Tìm m để A<0

Trả lời

$\begin{array}{l}a)A=\left[\frac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}-\frac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}\right]:\frac{2{\left(\sqrt{x}-1\right)}^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ =\frac{x+\sqrt{x}+1-x+\sqrt{x}-1}{\sqrt{x}}.\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{2{\left(\sqrt{x}-1\right)}^2}=\frac{2\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}.2\left(\sqrt{x}-1\right)}=\frac{\sqrt{x}+1}{\sqrt{x}-1}\\ b)A<0\iff \frac{\sqrt{x}+1}{\sqrt{x}-1}<0\Rightarrow \sqrt{x}-1<0\iff x<1\end{array}$