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Understanding One-Variable Rational Functions: Domain and Extraneous Solutions

This chapter explores solving equations involving rational expressions in one variable. It discusses what values make the rational expression defined and shows how to simplify, multiply, and add these expressions. Key examples guide you through canceling denominators and creating a common denominator for problem-solving. The importance of identifying extraneous solutions is emphasized, with practice problems that challenge you to solve equations and determine solutions not in the domain of the function. Master these concepts for a strong foundation in rational functions!

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Understanding One-Variable Rational Functions: Domain and Extraneous Solutions

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  1. Chapter 2: Polynomials, Power, and Rational Functions 2.7: Solving Equations in One Variable

  2. For what values is the rational expression defined? • Simplify the rational expression: • Multiply: • Add: Warm Up

  3. Example 1: • Example 2: Cancel the Denominator

  4. Example 3: Multiply both sides by both denominators. Create a Common Denominator

  5. Values you get when you solve for x that are NOT IN THE DOMAIN of the function. • In Example 3, what is the domain of f? • Which of the values for x are extraneous solutions? Extraneous Solutions

  6. 2. Practice Problems: Solve each equation, and identify any extraneous solutions.

  7. 3. 4. Practice Problems: Solve each equation, and identify any extraneous solutions.

  8. 2.7 #1-13 odd, 19, 23 Homework

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