Transcript Section 7.4
Chapter 7 Section 4 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 7.4 1 Equations with Rational Expressions and Graphs Solve rational equations. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley A rational equation is an equation that contains at least one rational expression with a variable in the denominator. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.4- 3 The easiest way to solve most rational equations is to multiply all terms in the equation by the least common denominator. This step will clear the equation of all denominators. It is necessary to either check the proposed solutions or verify that they are in the domain. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.4- 4 CAUTION When both sides of an equation are multiplied by a variable expression, the resulting proposed solutions may not satisfy the original equation. You must either determine and observe the domain or check all proposed solutions in the original equation. It is wise to do both. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.4- 5 EXAMPLE 1 Solve. 3 2 5 20 x 4 x Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.4- 6 EXAMPLE 2 Solve. 3 1 2 2 x 1 x 1 x 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.4- 7 EXAMPLE 3 Solve. 4 1 2 2 2 2 x x 6 x 4 x 5x 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.4- 8 EXAMPLE 4 Solve. 2 1 x 3x 2 x 3 x 1 x 2x 3 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.4- 9 EXAMPLE 5 Solve. 4 x 5 x Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.4- 10 EXAMPLE 6 Solve. y2 6 0 2 2 y y y 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.4- 11