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Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook

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2 Overview Section 6.1 in the textbook –Domain of rational expressions Find where a rational expression is undefined –Simplify rational expressions –Multiply rational expressions –Divide rational expressions

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Domain of Rational Expressions

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4 Domain: set of allowable values For now, we only care where the rational expression is UNDEFINED A rational expression can be viewed as a fraction –When is a fraction undefined? An exercise in factoring

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5 Domain of Rational Expressions (Example) Ex 1: Find where the following is undefined:

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6 Domain of Rational Expressions (Example) Ex 2: Find where the following is undefined:

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Simplify Rational Expressions

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8 Consider simplifying 20 / 30 –2 * 2 * 5 / 2 * 3 * 5 –2 / 3 Works the same way with rational expressions –Factor the numerator and denominator –Cross out common factors

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9 Simplify Rational Expressions (Example) Ex 3: Simplify

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10 Simplify Rational Expressions (Example) Ex 4: Simplify

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Multiply Rational Expressions

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12 Multiply Rational Expressions Consider multiplying 2 / 8 * 4 / 6 –Factor each numerator and denominator (2) / (2 * 2 * 2) * (2 * 2) / (2 * 3) –Cancel common factors between numerators and denominators (2) / (2 * 2 * 2) * (2 * 2) / (2 * 3) –Multiply to get the final answer 1 / 6

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13 Multiply Rational Expressions (Continued) Same process with rational expressions –Factor the numerator and denominator of each fraction –Cancel common factors –Multiply the remaining products for the final answer

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14 Multiply Rational Expressions (Example) Ex 5: Multiply

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15 Multiply Rational Expressions (Example) Ex 6: Multiply

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Divide Rational Expressions

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17 Divide Rational Expressions Consider dividing 2 / 8 ÷ 4 / 6 –Turn into a multiplication problem by flipping the second fraction 2 / 8 * 6 / 4 –Factor each numerator and denominator (2) / (2 * 2 * 2) * (2 * 3) / (2 * 2) –Cancel common factors between numerators and denominators (2) / (2 * 2 * 2) * (2 * 3) / (2 * 2) –Multiply to get the final answer 3 / 8

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18 Divide Rational Expressions (Continued) Same process with rational expressions –Turn into a multiplication problem by flipping the second rational expression –Factor the numerator and denominator of each fraction –Cancel common factors –Multiply the remaining products for the final answer

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19 Divide Rational Expressions (Example) Ex 7: Divide

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20 Divide Rational Expressions (Example) Ex 8: Divide

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21 Summary After studying these slides, you should know how to do the following: –Find the values that make a rational expression undefined –Simplify rational expressions –Multiply rational expressions –Divide rational expressions

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