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Solving Rational Equations: Strategies and Solutions Overview

This chapter discusses solving rational equations, including key concepts like finding the least common multiple (LCM) and identifying extraneous solutions. It specifically covers Problem 34, where the LCM is y² - 9, leading to the solutions 2 and 3, with 3 being discarded. The focus shifts to Problem 35 with an LCM of y² - 4, resulting in y = 5. Tips for solving these problems include checking for extraneous solutions, understanding multiple possible solutions, and writing steps down to avoid errors. This structured approach ensures clarity and accuracy in rational equation-solving.

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Solving Rational Equations: Strategies and Solutions Overview

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  1. Chapter 10.6 Solving Rational Equations Eric Fang Period 2

  2. Pg. 453, Problem 34 Solve LCM = y^2 – 9 so times equation by y^2 - 9 Collect like terms Simplify and set the equation to zero Next Slide

  3. Pg. 453, Problem 34 Cont’ Factor out the trinomial Using the Principle of Zero, the answer is 2 and 3. However, through checking, 3 is a extraneous and thus is crossed out. So the answer is 2

  4. Pg. 454, Problem 35 Solve. LCM is y^2 – 4 so times equation by y^2 - 4 Collect like terms Simplify Next Slide

  5. Pg. 454, Problem 35 Cont’ Simplify as stated last slide So y = 5

  6. Tips For better chances of getting these problems correct • Always check your work to see if your solution is an extraneous number. • It‘s better to try to uncover the extraneous solution at the beginning of tackling the problem so you know what numbers to avoid. • Chances are there may be more than one solution. • It is significantly easier if you write out the steps rather than do it all in your head.

  7. The End On the other hand, my resources come from the textbook, pg. 451 – 454.

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