Multiply and divide rational expressions.

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# Multiply and divide rational expressions. - PowerPoint PPT Presentation

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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Presentation Transcript

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 the numerators and denominators.

Factor.

Divide out the common factors.

Simplify.

Example 1B: Multiplying Rational Expressions

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.

Example 1C: Multiplying Rational Expressions

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

Remember!

See the Quotient of Powers Property

Check It Out! Example 1a

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

Simplify.

Divide out common factors. Use properties of exponents.

Check It Out! Example 1b

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

Simplify.

Divide out common factors. Use properties of exponents.

Write the polynomial over 1.

Factor the numerator and denominator.

Divide out common factors.

Multiply remaining factors.

Check It Out! Example 2

Write the polynomial over 1.

Factor the numerator and denominator.

Divide out common factors.

Multiply remaining factors.

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.

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.

Then multiply.

Example 3: Multiplying a Rational Expression Containing Polynomials

Method 1 Simplify first.

Factor.

Divide out common factors.

Simplify.

Example 3 Continued

Method 2 Multiply first.

Multiply.

Distribute.

Example 3 Continued

Then simplify.

Factor.

Divide out common factors.

Simplify.

Then multiply.

Check It Out! Example 3a

Simplify first.

Factor.

Divide out common factors.

Simplify.

Then multiply.

p

Check It Out! Example 3b

Simplify first.

Factor.

Divide out common factors.

Simplify.

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.

Example 4A: Dividing by Rational Expressions and Polynomials

Write as multiplication by the reciprocal.

Multiply the numerators and the denominators.

Divide out common factors.

Simplify.

Example 4B: Dividing by Rational Expressions and Polynomials

Write as multiplication by the reciprocal.

Factor. Rewrite one opposite binomial.

Example 4B Continued

Divide out common factors.

Simplify.

Example 4C: Dividing by Rational Expressions and Polynomials

Write the binomial over 1.

Write as multiplication by the reciprocal.

Multiply the numerators and the denominators.

Example 4C Continued

Divide out common factors.

Simplify.

Check It Out! Example 4a

Write as multiplication by the reciprocal.

Multiply the numerators and the denominators.

Simplify. There are no common factors.

Check It Out! Example 4b

Write as multiplication by the reciprocal.

Multiply the numerators and the denominators and cancel common factors.

Simplify.

Check It Out! Example 4c

Write the trinomial over 1.

Write as multiplication by the reciprocal.

Multiply.

Check It Out! Example 4c Continued