x < 0. Rút gọn biểu thức

B

- Hướng dẫn giải

VT

$$\begin{gathered} \sqrt{\frac{-2\sqrt{4+{\left(2^x-2^{-x}\right)}^2}}{2\sqrt{4+{\left(2^x-2^{-x}\right)}^2}}} \\ =\sqrt{\frac{-2\sqrt{2^{2x}+2^{-2x}+2}}{2\sqrt{2^{2x}+2^{-2x}+2}}} \\ =\sqrt{\frac{-2{\left(2^x+2^{-x}\right)}^2}{2{\left(2^x+2^{-x}\right)}^2}} \\ =\frac{\sqrt{2^x+2^{-x}-2}}{\sqrt{2^x+2^{-x}+2}} \\ =\frac{\sqrt{\left(2^{-{\displaystyle \frac{x}{2}}}-2^{{\displaystyle \frac{x}{2}}}\right)}}{\sqrt{\left(2^{-\frac{x}{2}}+2^{\frac{x}{2}}\right)}} \\ =\frac{\left(2^{-\frac{x}{2}}-2^{\frac{x}{2}}\right)}{\left(2^{-\frac{x}{2}}+2^{\frac{x}{2}}\right)} \\ =\frac{1-2^x}{1+2^x} \end{gathered}$$

Đáp án B