Originally Posted by

**Glitch** The question:

Find the limit as x tends to infinity $\displaystyle \sqrt{x^2 + x} - x$

I'm not sure how to go about it. I'm thinking that I need to get rid of that square root, or at least, get it in a form which will make it easy to read off the limit.

I've tried the following:

$\displaystyle \frac{\sqrt{x^2 + x} - x}{1} . \frac{\sqrt{x^2 + x} + x}{\sqrt{x^2 + x} + x}$

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

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

I'm not sure how to factor out x in the denominator, I'm guessing that'd simplify it.

If anyone could help, or offer a different method of solving this, I'd really appreciate it.