So I'm trying to evaluate $\lim \limits_{x\to -\infty} x + \sqrt{x^2+2x}$
These are my steps:
I first rationalize the expression (square root trick) - $$\lim \limits_{x\to -\infty} \frac{-2x}{x - \sqrt{x^2+2x}}$$ Then I simply divide by $x$ so $$\lim \limits_{x\to -\infty} \frac{-2}{1 - \sqrt{1+\frac{1}{2x}}}$$
Then I get the following by evaluating the limit $$\frac{-2}{1 - \sqrt{1}}$$ which then evaluates to $0$ in the denominator. Would really appreciate some help in understanding what I'm doing wrong here.
Thanks in advance!