1. Operations Multiplying Dividing
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2. Multiplying and Dividing Rational Expressions
7.2
Multiplying and Dividing Rational Expressions
Multiply rational expressions.
Divide rational expressions. 1 2
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3. Multiply rational expressions.
Objective 1
Multiply rational expressions.
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4. 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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5. EXAMPLE 1 Multiply. Write each answer in lowest terms. 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.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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6. EXAMPLE 2 Multiply. Write the answer in lowest terms. Solution:
Multiplying Rational Expressions
Multiply. Write the answer in lowest terms.
Solution:
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7. EXAMPLE 3 Solution: Multiply. Write the answer in lowest terms.
Deciding whether Ordered Pairs Are Solutions of an Equation
Multiply. Write the answer in lowest terms.
Solution:
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8. Divide rational expressions.
Objective 2
Divide rational expressions.
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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 Divide. Write each answer in lowest terms. Solution:
Dividing Rational Expressions
EXAMPLE 4
Divide. Write each answer in lowest terms.
Solution:
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11. EXAMPLE 5 Divide. Write the answer in lowest terms. Solution:
Dividing Rational Expressions
EXAMPLE 5
Divide. Write the answer in lowest terms.
Solution:
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12. EXAMPLE 6 Divide. Write the answer in lowest terms. Solution:
Dividing Rational Expressions
EXAMPLE 6
Divide. Write the answer in lowest terms.
Solution:
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13. EXAMPLE 7 Divide. Write in the answer in lowest terms. Solution:
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. Multiplying or Dividing Rational Expressions.
In summary, use the following steps to multiply or divide rational expressions.
Step 1: Note the operation. If the operation is division, use the definition of division to rewrite it as multiplication.
Step 2: Multiply numerators and denominators.
Step 3: Factor all numerators and denominators completely.
Step 4: Write in lowest terms using the fundamental property.
Steps 2 and 3 may be interchanged based on personal preference.
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