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5.5 Solving Rational Equations and Inequalities

5.5 Solving Rational Equations and Inequalities . Objective : Students will be able to solve rational equations and inequalities. . Vocabulary. **Remember that a rational expression is a quotient of two polynomials

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5.5 Solving Rational Equations and Inequalities

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  1. 5.5 Solving Rational Equations and Inequalities Objective: Students will be able to solve rational equations and inequalities.

  2. Vocabulary • **Remember that a rational expression is a quotient of two polynomials • Rational equation – an equation that contains one or more rational expressions. • Extraneous solution – a solution of a solved equation that is not a solution of the original equation. • Rational inequality – an inequality that contains one or more rational expressions.

  3. Part 1: Solving Rational Equations • To solve a rational equation, you must first multiply each term of the equation by the least common denominator (LCD) of all of the rational expressions in the equation. • Directions: Solve the equation. • Example 1:

  4. Example 2 … your turn • Solve

  5. Example 3 • Solve

  6. Example 4 … your turn • Solve

  7. Part 2: Extraneous Solutions • Example 5: Solve

  8. Example 6 • Solve

  9. Example 7 … your turn • Solve

  10. Homework for tonight • Homework # ____ • Textbook pg. 353 #19, 20, 22, 24, 25, 26

  11. Problem Solving Applications • Example 8: A kayaker spends an afternoon paddling on a river. She travels 3 miles upstream and 3 miles downstream in a total of 4 hours. In still water, the kayaker can travel at an average speed of 2 mi/h. Based on this information, what is the average speed of the river’s current?

  12. Example 9 • A jet travels 3950 miles from Chicago to London, and 3950 miles back from London to Chicago. The total flying time is 16.5 hours. The return trip takes longer due to winds that generally blow from west to east. If the jet’s average speed with no wind is 485 mi/h, what is the average speed of the wind during the round-trip flight? Round to the nearest mi/h.

  13. Example 10 • Jason can clean a large tank at an aquarium in about 6 hours. When Jason and Lacy work together, they can clean the tank in about 3.5 hours. About how long would it take Lacy to clean the tank if she works by herself?

  14. Example 11 • Julien can mulch a garden in 20 minutes. Together, Julien and Remy can mulch the same garden in 11 minutes. How long will it take Remy to mulch the garden when working alone? Round to the nearest minute.

  15. Homework for tonight • Homework # ______ • #1: On a different river, the kayaker travels 2 miles upstream and 2 miles downstream in a total of 5 hours. What is the average speed of the current of this river? Round to the nearest tenth. • Pg. 353 # 28 & 29

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