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Multiply and divide rational expressions.

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Multiply and divide rational expressions. - PowerPoint PPT Presentation


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Objective. Multiply and divide rational expressions. The rules for multiplying rational expressions are the same as the rules for multiplying fractions. You multiply the numerators, and you multiply the denominators. Example 1A: Multiplying Rational Expressions. Multiply. Simplify your answer.

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Objective

Multiply and divide rational expressions.

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The rules for multiplying rational expressions are the same as the rules for multiplying fractions. You multiply the numerators, and you multiply the denominators.

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Example 1A: Multiplying Rational Expressions

Multiply. Simplify your answer.

Multiply the numerators and denominators.

Factor.

Divide out the common factors.

Simplify.

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Example 1B: Multiplying Rational Expressions

Multiply. Simplify your answer.

Multiply the numerators and the denominators. Arrange the expression so like variables are together.

Simplify.

Divide out common factors. Use properties of exponents.

Simplify. Remember that z0 = 1.

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Example 1C: Multiplying Rational Expressions

Multiply. Simplify your answer.

Multiply. There are no common factors, so the product cannot be simplified.

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Remember!

See the Quotient of Powers Property

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Check It Out! Example 1a

Multiply. Simplify your answer.

Multiply the numerators and the denominators. Arrange the expression so like variables are together.

Simplify.

Divide out common factors. Use properties of exponents.

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Check It Out! Example 1b

Multiply. Simplify your answer.

Multiply the numerators and the denominators. Arrange the expression so like variables are together.

Simplify.

Divide out common factors. Use properties of exponents.

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Example 2: Multiplying a Rational Expression by a Polynomial.

Multiply . Simplify your answer.

Write the polynomial over 1.

Factor the numerator and denominator.

Divide out common factors.

Multiply remaining factors.

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Check It Out! Example 2

Multiply Simplify your answer.

Write the polynomial over 1.

Factor the numerator and denominator.

Divide out common factors.

Multiply remaining factors.

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Remember!

Just as you can write an integer as a fraction, you can write any expression as a rational expression by writing it with a denominator of 1.

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There are two methods for simplifying rational expressions. You can simplify first by dividing out and then multiply the remaining factors. You can also multiply first andthen simplify. Using either method will result in the same answer.

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Then multiply.

Example 3: Multiplying a Rational Expression Containing Polynomials

Multiply . Simplify your answer.

Method 1 Simplify first.

Factor.

Divide out common factors.

Simplify.

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Example 3 Continued

Method 2 Multiply first.

Multiply.

Distribute.

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Example 3 Continued

Then simplify.

Factor.

Divide out common factors.

Simplify.

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Then multiply.

Check It Out! Example 3a

Multiply . Simplify your answer.

Simplify first.

Factor.

Divide out common factors.

Simplify.

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Then multiply.

p

Check It Out! Example 3b

Multiply . Simplify your answer.

Simplify first.

Factor.

Divide out common factors.

Simplify.

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The rules for dividing rational expressions are the same as the rules for dividing fractions. To divide by a rational expression, multiply by its reciprocal.

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Example 4A: Dividing by Rational Expressions and Polynomials

Divide. Simplify your answer.

Write as multiplication by the reciprocal.

Multiply the numerators and the denominators.

Divide out common factors.

Simplify.

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Example 4B: Dividing by Rational Expressions and Polynomials

Divide. Simplify your answer.

Write as multiplication by the reciprocal.

Factor. Rewrite one opposite binomial.

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Example 4B Continued

Divide. Simplify your answer.

Divide out common factors.

Simplify.

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Example 4C: Dividing by Rational Expressions and Polynomials

Divide. Simplify your answer.

Write the binomial over 1.

Write as multiplication by the reciprocal.

Multiply the numerators and the denominators.

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Example 4C Continued

Divide. Simplify your answer.

Divide out common factors.

Simplify.

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Check It Out! Example 4a

Divide. Simplify your answer.

Write as multiplication by the reciprocal.

Multiply the numerators and the denominators.

Simplify. There are no common factors.

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Check It Out! Example 4b

Divide. Simplify your answer.

Write as multiplication by the reciprocal.

Multiply the numerators and the denominators and cancel common factors.

Simplify.

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Check It Out! Example 4c

Divide. Simplify your answer.

Write the trinomial over 1.

Write as multiplication by the reciprocal.

Multiply.

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Check It Out! Example 4c Continued

Divide. Simplify your answer.

Factor. Divide out common factors.

Simplify.

assignment

Assignment

p. 558 16-43

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