As the question title suggests, what is$$\lim_{x \to 0^+} \left({1\over{\sqrt{x}}} - {1\over{\sqrt{x^2 + x}}}\right)?$$WolframAlpha suggests that it should be $0$ according to a graph, but I'm not sure how to show this algebraically. Factoring out the $x$ in $x^2 + x$ and then trying to make the demominator the same of both terms didn't go anywhere. Any help would be well-appreciated.
This is before we cover derivatives (e.g. L'Hôpital's rule) in my calculus textbook, so there in theory should be a more elementary approach.
