Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 79: 17

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Given $$\lim _{x \rightarrow -\infty}\frac{x-2}{x^2+2x+1}$$ Then \begin{align*} \lim _{x \rightarrow -\infty}\frac{x-2}{x^2+2x+1}&=\lim _{x \rightarrow -\infty}\frac{x/x^2-2/x^2}{x^2/x^2+2x/x^2+1/x^2}\\ &=\lim _{x \rightarrow -\infty}\frac{1/x -2/x^2}{1+2 /x +1/x^2}\\ &=\frac{0-0}{1+0+0}\\ &=0 \end{align*}