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find the limits :$$\lim_{ x \to \infty}\frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x}+\sqrt{x+2}-\sqrt{4x+12}}$$

WolframAlpha gives me: $$\lim_{ x \to \infty }\frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x}+\sqrt{x+2}-\sqrt{4x+12}}=3/4$$

What is a simple way for the limits?

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    This seems to be the same question as [Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$](http://math.stackexchange.com/q/1854348). Found [using Approach0](https://approach0.xyz/search/?q=%24%5Clim_%7B%20x%20%5Cto%20%5Cinfty%20%7D%5Cfrac%7B%5Csqrt%7Bx%2B1%7D%2B%5Csqrt%7Bx%2B2%7D-%5Csqrt%7B4x%2B12%7D%7D%7B%5Csqrt%7Bx%7D%2B%5Csqrt%7Bx%2B2%7D-%5Csqrt%7B4x%2B12%7D%7D%24&p=1). – 2017-02-13

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