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LearninDaMath

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## Homework Statement

[itex]\stackrel{lim}{x\rightarrow}∞[/itex] [itex]\sqrt{x^2+x}-x[/itex]I'm taking the limit of a rational function as x approaches ∞. However, within the problem, there is an algebraic arrangement I'm having trouble with. How would I get from the first fraction to the second fraction?

Applying L'hopitals to: [itex]\frac{x}{\sqrt{x^2+x}+x}[/itex]

I get: [itex]\frac{1}{\frac{x+1}{x+\sqrt{x}}+1}[/itex]

But don't know how to get to: [itex]\frac{1}{\sqrt{1+\frac{1}{x}}+1}[/itex] ?

And the final solution simplified: 1/2