1. R.5 day2 Multiply and Divide Rational Expressions
Learning Target: You will be able to multiply and divide rational expressions, and simplify the product or quotient.

2. Multiply rational expressions.
The product of two fractions is found by multiplying the numerators and multiplying the denominators. Rational expressions are multiplied in the same way.
The product of the rational expressions and is
That is, to multiply rational expressions, multiply the numerators and multiply the denominators.
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3. EXAMPLE 1 Solution: Multiplying Rational Expressions
Multiply. Write each answer in lowest terms.
Solution:
It is also possible to divide out common factors in the numerator and denominator before multiplying the rational expressions.
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4. Multiply the fractions
Reduce before multiply.

5. Multiply the fractions
Reduce before multiply.

6. Example 2 Multiply rational expressions
Step 1: Factor and Multiply

7. Checkpoint Multiply the expression
6x² + 18x x² - x – 2 x² + x – 6 * x² - 7x – 8 6x(x + 3)(x-2)(x+1) (x+3)(x-2)(x-8)(x+1) 6x x-8

8. More Examples
Multiply the expressions. Simplify the result.

9. Divide rational expressions.
Division of rational expressions is defined as follows.
If and are any two rational expressions with then
That is, to divide one rational expression by another rational expression, multiply the first rational expression by the reciprocal of the second rational expression.
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10. EXAMPLE 4 Solution: Dividing Rational Expressions
Divide. Write each answer in lowest terms.
Solution:
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11. EXAMPLE 5 Solution: Dividing Rational Expressions
Divide. Write the answer in lowest terms.
Solution:
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12. EXAMPLE 6 Solution: Dividing Rational Expressions
Divide. Write the answer in lowest terms.
Solution:
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13. EXAMPLE 7
Dividing Rational Expressions (Factors Are Opposites)
Divide. Write in the answer in lowest terms.
Solution:
Remember to write −1 when dividing out factors that are opposite of each other. It may be written in the numerator or denominator, but not both.
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14. Divide the Rational Expressions
You can only Reduce when Multiplying

15. Example 4 Divide rational expressions
Step 1: Multiply by reciprocal
Step 2: Factor and Multiply
Step 3: Simplify

16. More Examples
Divide each expression. Simplify the result.

17. Homework
R.5 (pg 53) #33-49 odd