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Chapter 8: Rational and Radical Functions

Section 5: Solving Rational Equations and Inequalities. Chapter 8: Rational and Radical Functions. Objectives. Solve rational equations and inequalities. Vocabulary. rational equation extraneous solution rational inequality. Who Uses This?.

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Chapter 8: Rational and Radical Functions

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  1. Section 5: Solving Rational Equations and Inequalities Chapter 8: Rational and Radical Functions

  2. Objectives • Solve rational equations and inequalities.

  3. Vocabulary • rational equation • extraneous solution • rational inequality

  4. Who Uses This? • Kayakers can use rational equations to determine how fast a river is moving. • (See Example 3.)

  5. 8.5: Solving Rational Equations and Inequalities • A rational equation is an equation that contains one or more rational expressions. • The time t in hours that it takes to travel d miles can be determined by using the equation t = d/r , where r is the average rate of speed. • This equation is a rational equation.

  6. 8.5: Solving Rational Equations and Inequalities • To solve a rational equation, start by multiplying each term of the equation by the least common denominator (LCD) of all of the expressions in the equation. • This step eliminates the denominators of the rational expressions and results in an equation you can solve by using algebra.

  7. Example 1: Solving Rational Equations

  8. 8.5: Solving Rational Equations and Inequalities • An extraneous solution is a solution of an equation derived from an original equation that is not a solution of the original equation. • When you solve a rational equation, it is possible to get extraneous solutions. • These values should be eliminated from the solution set. • Always check your solutions by substituting them into the original equation.

  9. Example 2: Extraneous Solutions

  10. Example 3: Problem Solving Application

  11. Example 4: Work Application

  12. 8.5: Solving Rational Equations and Inequalities • A rational inequality is an inequality that contains one or more rational expressions. • One way to solve rational inequalities is by using graphs and tables.

  13. Example 5: Using Graphs and Tables to Solve Rational Equations and Inequalities

  14. 8.5: Solving Rational Equations and Inequalities • You can also solve rational inequalities algebraically. • You start by multiplying each term by the least common denominator (LCD) of all the expressions in the inequality. • However, you must consider two cases: the LCD is positive or the LCD is negative.

  15. Example 6: Solving Rational Inequalities Algebraically

  16. OTL • Page 605 • 1-10 • 13-27

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