2. Section 8-4 Multiplying and Dividing Rational Expressions

3. Objectives I can simplify rational expressions with multiplication I can simplify rational expressions with division

4. Review Key Concepts Factoring Methods –GCF –Reverse FOIL –Swing & Divide –Difference of 2 Squares

5. GCF 3x + 9 3(x + 3) Or (2 – x) -1(x – 2)

6. Reverse FOIL x 2 - x – 12 (x – 4)(x + 3)

7. Swing & Divide 3x 2 + 2x – 8 x 2 + 2x – 24 (x + 6)(x – 4) (x + 6/3)(x – 4/3) (x + 2)(3x – 4)

8. Difference of 2 Squares 16x 2 – 9 (4x + 3)(4x – 3)

9. Multiplying rational Expressions Usually you DON’T multiply, you just reduce 1. You will factor all numerators and denominators, then 2. Reduce or cancel like terms

10. Simplifying Property for Rational Expressions If a, b, and c are expressions with b and c not equal to zero, then

11. Example: Reducing

12. Example: Factoring

13. EXAMPLE 1 Simplify a rational expression x 2 – 2x – 15 x 2 – 9 Simplify : x 2 – 2x – 15 x 2 – 9 (x +3)(x –5) (x +3)(x –3) = Factor numerator and denominator. (x +3)(x –5) (x +3)(x –3) = Divide out common factor. Simplified form SOLUTION x – 5 x – 3 = ANSWER x – 5 x – 3

14. GUIDED PRACTICE for Examples 1 and 2 2x 2 + 10x 3x 2 + 16x + 5 6. 2x 2 + 10x 3x 2 + 16x + 5 (3x + 1)(x + 5) 2x(x + 5) = Factor numerator and denominator. Divide out common factor. 2x2x 3x + 1 = Simplified form (3x + 1)(x + 5) 2x(x + 5) = ANSWER 2x2x 3x + 1 SOLUTION

15. Dividing Rational Expressions We actually never want to divide rational expressions. Instead, turn them into multiplication problems to simplify by reducing To turn division into multiplication, simply change the sign and invert the 2 nd fraction

16. Division to Multiplication

17. Example

18. Handling Negatives

19. GUIDED PRACTICE for Examples 6 and 7 Divide the expressions. Simplify the result. 4x4x 5x – 20 x 2 – 2x x 2 – 6x + 8 11. 4x4x 5x – 20 x 2 – 2x x 2 – 6x + 8 Multiply by reciprocal. Divide out common factors. Factor. Simplified form 4x4x 5x – 20 x 2 – 2x x 2 – 6x + 8 = 4(x)(x – 4)(x – 2) 5(x – 4)(x)(x – 2) = 4(x)(x – 4)(x – 2) 5(x – 4)(x)(x – 2) = 4 5 = SOLUTION

20. Homework WS 12-4