University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

398

Pages:

6
Author:

orangejuiicehn17

Multiplying and Dividing Rational Expressions For use with Exploration 7.3 Essential Question: How can you determine the excluded values in a product or quotient of two rational expressions? 1 EXPLORATION: Multiplying and Dividing Rational Expressions Work with a partner. Find the product or quotient of the two rational expressions. Then match the product or quotient with its excluded values. Explain your reasoning. Product or Quotient 1/x * x-2/x+1 = 0 1/x-1 * -1/x-1 = 0 1/x-2 * x-2/x+1 = 0 x+2/x-1 * -x/x+2 = 0 x/x+2 * x+1/x+2 = 0 x/x-2 * x+1/x = 0 x/x+2 * x-1/x = 0 x+2/x * x+1/x-1 = 0 Property of Zero 5 + 0 = 5 5(0) = 0 0/5 = 0 and 5/0 ≠ 0 You cannot divide by zero! Excluded Values A. 0, and 2 B. 2 and -1 C. 0, and 1 D. -2 and 1 E. -1, 0, and 1 F. -1 and 1 G. 2 and -1 H. -2 and -1 7.3 Multiplying and Dividing Rational Expressions (continued) 2 EXPLORATION: Writing a Product or Quotient Work with a partner. Write a product or quotient of rational expressions that has the given excluded values. Justify your answer. 1 a. -1 (x+1) / (x-1) * -1 / (x+1) b. -1 and 3 -5 / (x+1) * x / (x-3) c. -1, 0, and 3 x / (x+1) / (x-3) / x Multiplying Rational Expressions Let a, b, c, and d be expressions with b ≠ 0 and d ≠ 0. Property: a/b * c/d = ac/bd Simplify ac/bd if possible. Example: 5x/2xy² * 6xy/10y = 30xy²/20xy³ = 10 * 3 * x * y² / 10 * 2 * x * y² * y = 3x/2y Reduce 5x/2xy² * 6xy/10y = 3x/2y Then multiply across 2/1 * 3/2 = 3x/2y Dividing Rational Expressions Let a, b, c, and d be expressions with b ≠ 0, c ≠ 0, and d ≠ 0. Property: a/b ÷ c/d = a/b * d/c = ad/bc Simplify ad/bc if possible. Example: 7/(x+1) ÷ (2x-3)/(x+2) = 7/(x+1) * (x+2)/(2x-3) = 7(x+2)/(x+1)(2x-3) Notetaking with Vocabulary For use after Lesson 7.3 In your own words, write the meaning of each vocabulary term. rational expression 1 is a fraction whose numerator and denominator are non-zero polynomials simplified form of a rational expression is when it's numerator and denominator have no common factors a/b and ax+b/x-c Core Concepts Simplifying Rational Expressions Let a, b, and c be expressions with b ≠ 0 and c ≠ 0. Property ac/bc = a/b Divide out common factor c Examples 15/65 = 3 * 5 / 13 * 5 = 3/13 Divide out common factor 5. 4(x+3) / (x+3)(x+3) = 4 / x+3 Divide out common factor x+3 *simplify can only happen if you are multiplying So 4/x+4 is not reduceable ...however 4/4x is reduceable