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Given this function: $y=\frac{x^4-3}{4x-1}$

Studying the sign of the function I get that it's positive when $x<\frac{1}{4}∨x>\sqrt[4]{3}$ and negative in the other way. Then why is the graph negative even in the lower left?

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Your solution is not complete. You have two roots $\pm \sqrt[4]{3}$...

Given function is negative for: $x< -\sqrt[4]{3}$ and ${1\over 4}<x<\sqrt[4]{3}$

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