Multiplying & Dividing Rational Expressions MATH 018 Combined Algebra S. Rook

2 Overview Section 7.2 in the textbook: –Multiply rational expressions –Divide rational expressions

3 Multiplying Rational Expressions

44 Consider multiplying 2 / 8 * 4 / 6 –Factor each numerator and denominator i.e. write the prime factorization –Divide out common factors between numerators and denominators –Multiply across to get the final answer 1/61/6

55 Multiplying Rational Expressions (Continued) Same process with rational expressions –Completely factor the numerator and denominator of each fraction –Divide out common factors Remember for polynomials other than a monomial, divide out either EVERYTHING or NOTHING AT ALL –Multiply the remaining factors for the final answer

Multiplying Rational Expressions (Example) Ex 1: Multiply and simplify: a) b) 6

7 Dividing Rational Expressions

88 Consider dividing 2 / 8 ÷ 4 / 6 –Convert into a multiplication problem by flipping the second fraction –Factor each numerator and denominator –Divide out common factors between numerators and denominators –Multiply to get the final answer 3/83/8

99 Dividing Rational Expressions (Continued) Same process with rational expressions –Convert into a multiplication problem by taking the reciprocal of the second rational expression –Completely factor the numerator and denominator of each fraction –Divide out common factors Remember for polynomials other than a monomial, divide out either EVERYTHING or NOTHING AT ALL –Multiply the remaining products for the final answer

Dividing Rational Expressions (Example) Ex 2: Divide and simplify: a) b) c) 10

11 Summary After studying these slides, you should know how to do the following: –Multiply rational expressions –Divide rational expressions Additional Practice –See the list of suggested problems for 7.2 Next lesson –Adding & Subtracting Rational Expressions with the Same Denominator (Section 7.3)