1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2.8 Solving Equations in One Variable

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 3 Quick Review

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 4 Quick Review Solutions

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 5 What you’ll learn about Solving Rational Equations Extraneous Solutions Applications … and why Applications involving rational functions as models often require that an equation involving fractions be solved.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 6 Example Solving by Clearing Fractions

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 7 Example Solving by Clearing Fractions

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solving a Rational Equation Slide 2- 8

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solve Graphically The graph in Figure 2.56 suggests that the function has two zeros. We can use the graph to find that the zeros are about 0.268 and 3.732, agreeing with the values found algebraically. Solving a Rational Equation Slide 2- 9

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 10 Extraneous Solutions When we multiply or divide an equation by an expression containing variables, the resulting equation may have solutions that are not solutions of the original equation. These are extraneous solutions. For this reason we must check each solution of the resulting equation in the original equation.

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 11 Example Eliminating Extraneous Solutions

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 12 Example Eliminating Extraneous Solutions

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 13 Example Eliminating Extraneous Solutions

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Calculating Acid Mixtures Slide 2- 14 How much pure acid must be added to 50 mL of a 35% acid solution to produce a mixture that is 75% acid?

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Calculating Acid Mixtures Slide 2- 15 How much pure acid must be added to 50 mL of a 35% acid solution to produce a mixture that is 75% acid?

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 16

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 17

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 18 Example Finding a Minimum Perimeter

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 19 Example Finding a Minimum Perimeter

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 20

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Designing a Juice Can Slide 2- 21 Stewart Cannery will package tomato juice in 2-liter cylindrical cans. Find the radius and height of the cans if the cans have a surface area of 1000 cm 2. (1 liter = 1000 cm 3) Model S = surface area of can in cm 2 r = radius of can in centimeters h = height of can in centimeters

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 22 Designing a Juice Can

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 23 Designing a Juice Can

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 24 pg 254:,#1-35 odd