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Chapter 6 Section 6

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Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solving Equations with Rational Expressions Distinguish between operations with rational expressions and equations with terms that are rational expressions. Solve equations with rational expressions. Solve a formula for a specified variable. 6.6 2 3

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Distinguish between rational expressions and equations Slide 6.6-3

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Distinguish between expressions and equations Slide 6.6-4 Expressions Equations Numbers Operations Variables NO equal signEqual sign Simplify Solve Uses of the LCD When adding or subtracting rational expressions, find the LCD, then add numerators When simplifying a complex fraction, multiply numerator and denominator by the LCD When solving an equation, multiply each side by the LCD so the denominators are eliminated. WOW the LCD is useful!

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Identify each of the following as an expression or an equation. Then simplify the expression or solve the equation. equation expression Slide 6.6-5 Distinguishing between Expressions and Equations CLASSROOM EXAMPLE 1

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Solve equations with rational expressions. Slide 6.6-6

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve equations with rational expressions When an equation involves fractions use the multiplication property of equality to clear the fractions choose as multiplier the LCD of all denominators in the fractions of the equation Please recall: The 11 th Commandment Thou shall not… divide by zero The denominator of a rational expression cannot equal 0, since division by 0 is undefined. Therefore, when solving an equation with rational expressions that have variables in the denominator, The solution cannot be a number that makes the denominator equal 0. Slide 6.6-7

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve, and check the solution. Solution: Check: Multiply every term of the equation by the LCD Slide 6.6-8 Solving an Equation with Rational Expressions CLASSROOM EXAMPLE 2

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solving an Equation with Rational Expressions Step 1: Multiply each side of the equation by the LCD to clear the equation of fractions. Be sure to distribute to every term on both sides. Step 2: Solve the resulting equation. Step 3: Check each proposed solution by substituting it into the original equation. Reject any solutions that cause a denominator to equal 0. Slide 6.6-9

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Solve, and check the proposed solution. Reject this solution. WHY?? Slide 6.6-10 Solving an Equation with Rational Expressions CLASSROOM EXAMPLE 3 How do you recognize equations that could possibly have restrictions?

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Solve, and check the proposed solution. The solution set is {4}. Slide 6.6-11 Solving an Equation with Rational Expressions CLASSROOM EXAMPLE 4 It works!

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Solve, and check the proposed solution. Does it work?? Slide 6.6-12 Solving an Equation with Rational Expressions CLASSROOM EXAMPLE 5 The solution set is {0}.

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve, and check the proposed solution (s). Solution: The solution set is {−4, −1}. or Slide 6.6-13 Solving an Equation with Rational Expressions CLASSROOM EXAMPLE 6

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve, and check the proposed solution. Solution: The solution set is {60}. Slide 6.6-14 Solving an Equation with Rational Expressions CLASSROOM EXAMPLE 7

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 3 Solve a formula for a specified variable. Slide 6.6-15

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve the following formula for z. Solution: Fun! Slide 6.6-17 Solving for a Specified Variable CLASSROOM EXAMPLE 9

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Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve each formula for the specified variable. Solution: Remember to treat the variable for which you are solving as if it were the only variable, and all others as if they were contants. Slide 6.6-16 You Try It CLASSROOM EXAMPLE 8

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