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**= 6x2 – 5x – 21 = x2 – 121 = 5(2x + 5) = 7x(4x + 5) = (x2 + 4) (x + 2)**

Find the product. (2x + 3)(3x – 7) (x – 11)(x + 11) = 6x2 – 5x – 21 = x2 – 121 Factor. 3. 10x + 25 4. 28x2 + 35x 5. x3 + 2x2 + 4x + 8 = 5(2x + 5) = 7x(4x + 5) = (x2 + 4) (x + 2) x2 + 11x + 30 7. x2 – 4x – 32 = (x + 6) (x + 5) = (x + 4) (x – 8)

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**More warm-up Solve the following equation (USE Factoring)**

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More Warm-up Simplify the fraction Standard: MM1A3e

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**Simplifying rational expressions**

A fraction whose numerator and denominator are nonzero polynomials Standard: MM1A3e

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Simplest Form When a rational expression’s numerator and denominator have no factors in common (other than 1). Process: Factor, then cancel. Standard: MM1A3e

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**1. Simplify a Rational Expression**

Reduce the numbers and subtract the exponents. Where the larger one is, is where the leftovers go. Standard: MM1A3e

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**2. Simplify a Rational Expression**

Factor the top Cross out the common factor x. Standard: MM1A3e

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**3. Simplify a Rational Expression**

Factor the bottom Cross out the common factor x. Standard: MM1A3e

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**4. Simplify a Rational Expression**

Factor the top Cross out the common factors of 5 and x. Standard: MM1A3e

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**5. Simplify a Rational Expression**

Factor the top and bottom Cross out the common factor (x + 4) Standard: MM1A3e

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**Recognize Opposite Factors**

When you have opposite factors, you will have to factor out a negative so that you can cancel. Standard: MM1A3e

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**6. Opposite Factors Factor the bottom**

(1 – x) on the top and (x – 1) on the bottom are opposites. Factor out a negative so they will cancel. Standard: MM1A3e

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Practice #7 Standard: MM1A3e

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Practice #8 Standard: MM1A3e

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Practice #9 Standard: MM1A3e

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Practice #10 Standard: MM1A3e

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Practice #11 Standard: MM1A3e

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Practice #12 Standard: MM1A3e

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9.1 Multiplying and Dividing Rational Expressions ©2001 by R. Villar All Rights Reserved.

9.1 Multiplying and Dividing Rational Expressions ©2001 by R. Villar All Rights Reserved.

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