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Chapter 11: Problem 80

What is a rational inequality?

Short Answer

Expert verified
A rational inequality is an inequality that involves a rational expression. It is solved by getting zero on one side of the inequality, finding critical points where the numerator or denominator equals zero, then determining where the rational expression is greater or less than zero.

Step by step solution

01

Definition

A rational inequality is like a rational equation, but instead of equality, there is an inequality sign. This sign can be less than (<), less than or equal to (鈮�), greater than (>), greater than or equal to (鈮�).
02

Examples of Rational Inequalities

Here are some examples of rational inequalities: 1) \(\frac{x}{x+1} > 0\), 2) \(\frac{3x+1}{2x-7} 鈮� 0\), 3) \(\frac{x^2-9}{x^2+2x-3} < 0\).
03

Solving Rational Inequalities

When solving rational inequalities, you'll first want to get zero on one side of the inequality. Then, you'll need to find the critical points of the equation, which occur at the x-values where the numerator or the denominator equals zero. Depending on the sign of the inequality, you'll be interested in the intervals where the rational expression is greater than zero (above the x-axis) or less than zero (below the x-axis).

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