A rational inequality is an inequality that contains a rational expression/09%3A_Rational_Expressions_and_Functions/9.07%3A_Solve_Rational_Inequalities). Rational inequalities are solved using many of the techniques used to solve linear inequalities, with some differences. When solving a rational inequality, we must remember that when we multiply or divide by a negative number, the inequality sign must reverse. We must also carefully consider what value might make the rational expression undefined and so must be excluded/09%3A_Rational_Expressions_and_Functions/9.07%3A_Solve_Rational_Inequalities). To solve a rational inequality, we first must write the inequality with only one quotient on the left and 0 on the right. Next, we determine the critical points to use to divide the number line into intervals. A critical point is a number that makes the rational expression zero or undefined. We then evaluate the factors of the numerator and denominator and find the quotient in each interval. This will identify the interval or intervals that contain all the solutions of the rational inequality. We write the solution in interval notation/09%3A_Rational_Expressions_and_Functions/9.07%3A_Solve_Rational_Inequalities).