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Understanding Rational Equations: Techniques and Cautions in Solving

This overview focuses on solving rational equations as outlined in Section 8.6. Key strategies include multiplication, adding and subtracting, and cross-multiplying to find solutions. Emphasis is placed on graphing techniques to visualize solutions, ensuring to check for asymptotes that could affect answers. Not all equations yield solutions, and some may require the quadratic formula. Essential practice assignments from page 593 are provided to solidify understanding and tackle various problems encountered in this section.

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Understanding Rational Equations: Techniques and Cautions in Solving

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  1. WarmupAlg227Mar 2012

  2. Agenda • Don't forget about resources on mrwaddell.net • Section 8.6: Solving Rational Equations • Multiplication • Adding & Subtracting • Cross multiplying • So we can solve

  3. Section 8.6: Solving Rational EQUATIONS

  4. Solving Equations by GRAPHING Step 1: put each side in calculator on it’s own line. Make sure you use parenthesis Step 2: See where they cross. Step 3: Eliminate Asymptotes if needed.

  5. x = 2, x = 3 x/(x-6) 1/(x-4) Zoom in

  6. Solving Equations - Algebra Step 1: Find the asymptotes! x=6, x=4. Our answer CANNOT be one of these. Step 2: Cross Multiply Step 3: Distribute Step 4: Solve Since x=2, and x=3 are not Asymp. We have 2 answers.

  7. Solving Equations - Algebra Step 1: Find the asymptotes! x=+3, x=-3. Our answer CANNOT be one of these. Step 2: Distribute & Add Step 3: make it equal zero

  8. Solving Equations - Algebra x=+3, x=-3. Our answer CANNOT be one of these. Step 4: factor or use quadratic formula. Since x=3 cannot be an answer, x = -2 is the only answer!

  9. Some Cautions • Not every equation has an answer. Some equations have “No Solution”. • You will need to use the quadratic formula on some of the problems. They are not always factorable. • Whenever there is a question, GRAPH IT! The picture never lies.

  10. Assignment • Section 8.6, page 593: • 7 – 11, • 15 – 22

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