Giải thích các bước giải:
$\lim_{x\to+\infty}(x-\sqrt{x^2+x+1})$
$=\lim_{x\to+\infty}\dfrac{x^2-(x^2+x+1)}{x+\sqrt{x^2+x+1}}$
$=\lim_{x\to+\infty}-\dfrac{x+1}{x+\sqrt{x^2+x+1}}$
$=\lim_{x\to+\infty}-\dfrac{1+\dfrac1x}{1+\sqrt{1+\dfrac1x+\dfrac1{x^2}}}$
$=-\dfrac{1+0}{1+\sqrt{1+0+0}}$
$=-\dfrac12$