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# Quiz 8-5

Quiz 8-5. Simplify. 1. 2. 8-6 Solve Rational Equations. Vocabulary:. What does solve a single variable equation mean?. 3x + 2 = 11. What is a factor?. What is a least common multiple ?. Solving Rational Equations. Method #1: eliminate the denominators one at a time.

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## Quiz 8-5

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### Presentation Transcript

1. Quiz 8-5 Simplify 1. 2.

2. 8-6 Solve Rational Equations

3. Vocabulary: What does solve a single variable equation mean? 3x + 2 = 11 What is a factor? What is a least common multiple?

4. Solving Rational Equations Method #1: eliminate the denominators one at a time. Method #2: Obtain common denominators for each term. Method #3: Find the least common multiple of all the denominators then multiply (left/right) by the LCM.

5. Rational Equations How do you get the ‘5’ out of the denominator? x = 20 Multiply both sides by ‘5’ How do you get the ‘x’ out of the denominator? 2x = 10 Multiply both sides by ‘x’ x = ?

6. Your turn: 1. Solve 2. Solve 3. Solve 4. Solve

7. Variable on both sides of the equation How do you get the ‘x’ out of the left-side denominator? Multiply both sides by ‘x’ How do you get the (x+1) out of the right-side denominator? Multiply both sides by (x+1) Your turn: 5. solve

8. Another example: The book teaches you to “cross-multiply” (yuck!) There is no property called “cross multiply”. There are the properties of equality. Cross multiplication is the result of multiplying both sides by the left denominator, then multiplying the both sides by the right denominator. DON’T THINK Cross multiply!! Forget it completely!!

9. Eliminate one Denomiator at a time. * (4x + 5) (4x + 5) * (x + 1) * * (x + 1)

10. Or: obtain a common denominator * (x + 1) (4x + 5) * (4x + 5) * * (x + 1) Multiply both sides by the common denominator

11. Your Turn: 6. Solve 7. Solve 8. Solve

12. What about this wrinkle? “multiply to eliminate the denominators one at a time” * x x * Now what? It’s a quadratic, solve the quadratic! put into standard form !!! Your turn: 9. solve

13. Rational equations with 2 solutions. What values of ‘x’ are not allowed? Your turn:10. Eliminate the denominator.