 ## Tutoring on Solving Rational Inequalities

Learning Objectives:

#### Understand to Solve Rational Inequalities

Math Tutoring on Solving Rational Inequalities

A rational inequality would be any inequality that fits the form a(x)/b(x) ˃0, the inequality symbol can be different. Following are the steps to follow to solve rational inequality.                                                                                                                                                                                                                                                                                                                                 1. If a rational inequality is not in this form, we have to put it in this form so that a single rational expression here on the left is compared to 0.

2. So once we have the inequality in this form, we are going to factor the numerator and denominator.

3. Then we will determine the zeroes of the numerator and denominator.

4. Then we will plot these zeroes on the number line. But the zeroes of the numerator can be either at closed points or open points, based upon the inequality symbol. The zeroes of the denominator will always be open points because we must exclude these values, because this is where we would have division by zero.

5. Once we form the intervals, we will test the intervals to determine the solution. Also, want to mention that we can solve rational inequalities by analyzing the graph of y = a(x)/b(x).

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Hook Questions:

1.     What is a rational inequality?

2.    What is the definition of rational equations?

3.    What is an example of a rational expression?

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