Lesson 5: Solving Rational Equations & Real-World Applications

• How do we solve rational equations?
• What does it mean to clear denominators?
• Why do we check for extraneous solutions?
• Where do rational equations appear in real life?

Rational equation, clear denominators, multiply by LCD, extraneous solution, verify

CCSS.MATH.9.A.REI.B.4

Description: Students solve rational equations by multiplying both sides by the LCD to clear denominators, creating polynomial equations they can solve. They check for extraneous solutions (values that were restrictions). Real-world applications (work problems, rate problems) show relevance. Purpose: To develop procedural fluency in solving rational equations and show real-world applications. DOK Level: 2-3 (Application)

• Real-world contexts: Work problems, rate problems, mixture problems
• For struggling learners: Solve equations with simple denominators
• For advanced learners: Solve more complex equations
• Extraneous solutions guide: Emphasize checking

• Observation: Do students multiply by LCD correctly?

• Worksheet: Solve 4 rational equations

• Check-your-work: Verify solutions and identify extraneous solutions

• Real-world problem: Solve a context-based rational equation

• Rational equation solving step-by-step guides

• LCD-finding review

• Extraneous solutions explanation

• Practice worksheets

• Real-world context cards

• Resource: Khan Academy "Solving Rational Equations" (adapted)