1. 1 Topic 8.2.1 Multiplying Rational Expressions Multiplying Rational Expressions

2. 2 Lesson 1.1.1 California Standard: 13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques. What it means for you: You’ll multiply rational expressions by factoring and cancelling. Topic 8.2.1 Key words: rational nonzero common factor Multiplying Rational Expressions

3. 3 Lesson 1.1.1 In Section 8.1 you learned about simplifying rational expressions. Topic 8.2.1 In this Topic you’ll learn to multiply rational expressions, but then you’ll use the same simplification methods to express your solutions in their simplest forms. Multiplying Rational Expressions

4. 4 Lesson 1.1.1 Multiplying by Rational Expressions Topic 8.2.1 Given any nonzero expressions m, c, b, and v : That is, the product of two rational expressions is the product of the numerators divided by the product of the denominators. Multiplying Rational Expressions

5. 5 Lesson 1.1.1 Multiplying by Rational Expressions Topic 8.2.1 These expressions can often be quite complicated, so simplify them as much as you can before multiplying. First, factor the numerators and denominators (if possible). Then find any factors that are common to both the top line (the numerator) and the bottom line (the denominator) and cancel them before multiplying. Multiplying Rational Expressions

6. 6 Example 1 Topic 8.2.1 Simplify. Solution Step 1: Factor the numerators and denominators. Solution follows… Step 2: Cancel all the common factors and multiply. = 1 1 1 1 1 1 = = Multiplying Rational Expressions

7. 7 Example 2 Topic 8.2.1 Solution Step 1: Factor the numerators and denominators if possible. Solution follows… = – Step 2: Cancel all the common factors and multiply. 1 1 1 2 Multiply and simplify. = = = 1 1 1 1 1 1 Multiplying Rational Expressions

8. 8 Multiply and simplify the rational expressions. 1. 2. 3.4. 5. 6. Lesson 1.1.1 Guided Practice Topic 8.2.1 Solution follows… Multiplying Rational Expressions

9. 9 Lesson 1.1.1 Topic 8.2.1 You can extend this concept to the multiplication of any number of rational expressions, with any number of variables. Multiplying Rational Expressions

10. 10 Example 3 Topic 8.2.1 Solution Factor the numerators and denominators, and cancel all the common factors and multiply. Solution follows… = or Simplify. = = 11111 11111 1 1 Multiplying Rational Expressions

11. 11 Example 4 Topic 8.2.1 Solution Factor the numerators and denominators, then cancel all the common factors and multiply. Solution follows… Simplify. = or = 1 1 111 111 Multiplying Rational Expressions

12. 12 Multiply and simplify the rational expressions. 7. 8. 9. Lesson 1.1.1 Guided Practice Topic 8.2.1 Solution follows… x – 5 2( m + 1) or 2 m + 2 Multiplying Rational Expressions

13. 13 Multiply and simplify the rational expressions. 1. 2. 3. 4. Independent Practice Solution follows… Topic 8.2.1 1 Multiplying Rational Expressions

14. 14 Multiply and simplify the rational expressions. 5. 6. 7. Independent Practice Solution follows… Topic 8.2.1 Multiplying Rational Expressions

15. 15 Topic 8.2.1 Round Up Multiplying Rational Expressions Usually the most difficult thing when solving problems like these is factoring the numerators and denominators. Look for “difference of two squares” expressions, perfect squares, and minus signs that you can factor outside the parentheses.