Answer
I would consider \lim_{x \to \infty} \sqrt{x^4-3x^2-1}-x^2
as \lim_{x \to \infty} \dfrac{\sqrt{x^4-3x^2-1}-x^2}{1}
Then multiply \sqrt{x^4-3x^2-1}+x^2 top and bottom to get rid of the ridiculous looking square root sign on the top. Then bingo!
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