Chapter 6 Rational Expressions and Equations Copyright 2015

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Chapter 6 Rational Expressions and Equations Copyright © 2015, 2011, 2007 Pearson Education, Inc.

Chapter 6 Rational Expressions and Equations Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6 -

Chapter Sections 6. 1 – The Domains of Rational Functions and Multiplication and Division

Chapter Sections 6. 1 – The Domains of Rational Functions and Multiplication and Division of Rational Expressions 6. 2 – Addition and Subtraction of Rational Expressions 6. 3 – Complex Fractions 6. 4 – Solving Rational Equations 6. 5 – Rational Equations: Applications and Problem Solving 6. 6 – Variation Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6 -2 2

§ 6. 4 Solving Rational Equations Copyright © 2015, 2011, 2007 Pearson Education, Inc.

§ 6. 4 Solving Rational Equations Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6 -

Solve Rational Equations A rational equation is an equation that contains at least one

Solve Rational Equations A rational equation is an equation that contains at least one rational expression. Examples: Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6 -4 4

Solve Rational Equations To Solve Rational Equations 1. Determine the LCD of all rational

Solve Rational Equations To Solve Rational Equations 1. Determine the LCD of all rational expressions in the equation. 2. Multiply both sides of the equation by the LCD. This will result in every term in the equation being multiplied by the LCD. This will eliminate all of the fractions from the equation. 3. Remove any parentheses and combine like terms on each side of the equation. 4. Solve the equation using the properties discussed in earlier sections. 5. Check the solution in the original equation. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6 -5 5

Solve Rational Equations Example Solve Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter

Solve Rational Equations Example Solve Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6 -6 6

Check Solutions When solving a rational equation with a variable in any denominator, you

Check Solutions When solving a rational equation with a variable in any denominator, you must check the value(s) obtained in the original equation. Since division by 0 is undefined, the value that makes a denominator 0 is not a solution and is called an extraneous solution. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6 -7 7

Solve Proportions Proportion A proportion is an equation of the form Proportions may also

Solve Proportions Proportion A proportion is an equation of the form Proportions may also be solved by crossmultiplication as follows: Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6 -8 8

Solve Proportions Similar Figures Similar figures are figures whose corresponding angles are equal and

Solve Proportions Similar Figures Similar figures are figures whose corresponding angles are equal and whose corresponding sides are in proportion Examples: Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6 -9 9

Example Triangles ABC and A’B’C’ are similar figures. Find the length of sides AB

Example Triangles ABC and A’B’C’ are similar figures. Find the length of sides AB and B’C’. Since a length of the side cannot be a negative number, -5 is not a possible answer. Substituting 6 for x, we see that the length of side B’C’ is 6 and the length of side AB is 6 -1 or 5. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6 -10 10

Solve Problems Involving Rational Functions Example Consider the function a for which f(a) =

Solve Problems Involving Rational Functions Example Consider the function a for which f(a) = 1. Copyright © 2015, 2011, 2007 Pearson Education, Inc. . Find all Chapter 6 -11 11