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Aaronmariano_
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Tyro
Asked: 2021-04-09T10:22:27+00:00 In: ,

rational inequalities

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How to solve rational inequalities

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  2. acedstud

    We solve rational inequalities just the same way we solve rational equations, however, we have to take note of the sign of the LCD when we multiply through as multiplying an inequality sign with a negative number changes the orientation of the inequality sign.

    For example, if we have \dfrac{x}{x+2}>\dfrac{1}{x}. The LCD is x(x+2), so we multiply through by the LCD to have x(x+2)\dfrac{x}{x+2}>x(x+2)\dfrac{1}{x}\Rightarrow x^2>x+2\Rightarrow x^2-x-2>0.

    Solving the quadratic inequality we have x>2 or x<-1.

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