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- Hướng dẫn giải

$\begin{array}{l}\underset{x\to +\infty }{\lim }\left(\sqrt{x^2-x+1}-\sqrt{x^2+x+1}\right)\\ =\underset{x\to +\infty }{\lim }\frac{-2x}{\sqrt{x^2-x+1}+\sqrt{x^2+x+1}}\\ =\underset{x\to +\infty }{\lim }\frac{-2x}{x\sqrt{1-\frac{1}{x}+\text{\hspace{0.17em}}\frac{1}{x^2}}+x\sqrt{1+\text{\hspace{0.17em}}\frac{1}{x}+\text{}\frac{1}{x^2}}}\\ =\underset{x\to +\infty }{\lim }\frac{-2}{\sqrt{1-\frac{1}{x}+\text{\hspace{0.17em}}\frac{1}{x^2}}+\sqrt{1+\text{\hspace{0.17em}}\frac{1}{x}+\text{}\frac{1}{x^2}}}=-1\end{array}$

Chọn đáp án D