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# Limit with negative square roots

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I'm having some trouble rationalizing and getting the answer from this limit

$$\lim_{x\rightarrow -\infty}\sqrt{5x^2+4x+7}-\sqrt{5x^2+x+3}$$

If rationalizing is the way to go, I've managed to get to (if even that's correct)

$$\lim_{x\rightarrow -\infty}\frac{3x+4}{\sqrt{5x^2+4x+7}+\sqrt{5x^2+x+3}}$$

I've not figured out a way yet to get 1 as the denominator and i'm a bit stuck

any help would be great

Jan 18, 2020