Hey,

Basically I have attempted a solution to my problem, it did not get the correct answer and I cannot figure out how to get the correct answer. Looking for where I am making my mistake and how to correct it!

Question

Find the limit

$\displaystyle \lim_{x\to -\infty} (x + \sqrt{x^2 + 2x}) $

Attempted solution:

*pretend that $\displaystyle \lim_{x\to -\infty} $ is in front, I am making a mess trying to coordinate this with that and it's just easier to show without..

$\displaystyle (x + \sqrt{x^2 + 2x})* \frac{(x - \sqrt{x^2 + 2x})}{(x - \sqrt{x^2 + 2x})} $ ***Multiplied by conjugate

$\displaystyle \frac{-2x}{x - \sqrt{x^2 + 2x}} $

The highest value of x is "x" so I divide that through the numerator and denominator and get:

$\displaystyle \frac{-2}{1 - \sqrt{1}} $

Which is giving me 0 on the bottom. I do not know how to fix this and was hoping someone could give me a hand here.

Thanks alot!