<s>[INST] Finding the limit of ${x+\sqrt{x^2-4x+1}}$ at negative infinity I'm having trouble finding the following limit:
\begin{equation}
\lim_{x \to -\infty} {x+\sqrt{x^2-4x+1}}
\end{equation}
I tried to simplify it in many ways but couldn't get it to a form where I could evaluate the limit. How should I go about modifying this limit in order to evaluate it? 
EDIT: Forgot the minus sign in front of the infinite, sorry.
 [/INST] $\displaystyle \lim_{x\to-\infty}x+\sqrt{x^2-4x+1}=\lim_{x\to-\infty}\frac{(x+\sqrt{x^2-4x+1})(x-\sqrt{x^2-4x+1})}{x-\sqrt{x^2-4x+1}}= \\ =\displaystyle \lim_{x\to-\infty}\frac{x^2-x^2+4x-1}{x-\sqrt{x^2-4x+1}}=\lim_{x\to-\infty}\frac{4-\frac{1}{x}}{1-\frac{|x|}{x}\sqrt{1-\frac{4}{x}+\frac{1}{x^2}}}=\frac{4}{2}=2$
</s>