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

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

Domain of Rational Expressions

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

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

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

Simplify Rational Expressions

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

9 Simplify Rational Expressions (Example) Ex 3: Simplify

10 Simplify Rational Expressions (Example) Ex 4: Simplify

Multiply Rational Expressions

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

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

14 Multiply Rational Expressions (Example) Ex 5: Multiply

15 Multiply Rational Expressions (Example) Ex 6: Multiply

Divide Rational Expressions

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

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

19 Divide Rational Expressions (Example) Ex 7: Divide

20 Divide Rational Expressions (Example) Ex 8: Divide

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