Lesson 6: 7-6 Solving Rational Equations and Inequalities

1. How would you solve a rational equation or rational inequality?
2. What is an extraneous solution?
3. What is an important step in solving rational equations or rational inequalities?

Rational Equation
Weighted Average
Rational Inequality

A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

SAT questions related to rational functions: 1-3-13, 6-3-12

During the solution process, a rational equation is usually transformed into another type of equation. Solving a rational equation may require solving a related linear, quadratic, or other type of equation.

A gaming club charges $20 per month for membership. Members also have to pay $5 each time they visit the club. If a member visits the club x times in one month, then the charge for that month will be 20+5x. The actual cost per visit will be (20+5x)/x. To determine how many visits are needed for the cost per visit to be $6, you would need to solve the equation (20+5x)/x=6.

Remind students that a possible solution must always be checked in the original equation, rather than in any of the steps of the solution.

Make sure that students understand the difference between the solutions of the quadratic equation (of which there are two) and the solution of the problem (of which there is only one) when applicable.

When solving rational equations, students often forget that all terms in the equation must be multiplied by the LCD. Remind them to do so in order to obtain equivalent equations.

Suggest that when a problem involves completing part of a job while working together, students think about what part of the work gets done in one day, or one year, or one unit of the time.

Suggest that students also verify whether the boundary indicated by the solution of the equation is or is not in the solution set of the inequality.

Have students think about the difference between "pure" mathematics, such as solving an equation, and "applied" mathematics, such as solving a real-world problem. Ask them to list some ways in which these two are alike and some ways in which they are different.

McGraw Hill resources

McGraw Hill resources