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Rational inequalities

A rational inequality is solved with a sign chart, not by multiplying through by the denominator. You do not know whether the denominator is positive or negative, and a negative number would flip the sign. Zeros of the numerator may be included when the inequality is $\ge$ or $\le$. Zeros of the denominator are never included, because the fraction is not defined there.

Symbols

Example

$\frac{x + 3}{x - 1} \ge 0$. For $x = 0$: $\frac{3}{-1} = -3$. For $x = 2$: $\frac{5}{1} = 5$. For $x = -4$: $\frac{-1}{-5} = 0.2$. The solution is $x \le -3$ or $x > 1$.

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Part of Mathematics 1T: Inequalities and sign charts.