1. In multiplying rational expressions, we use the following rule: Dividing by a rational expression is the same as multiplying by its reciprocal. 5.2 Multiplying and Dividing Rational Expressions.

2. To multiply rational expressions we use the following steps: 1.Multiply the numerator and multiply the denominator. 2.Factor completely the numerator and the denominator. 3. Cancel common factors and simplify

3. Multiply: Factor 16 and use product rule to multiply. Cancel common factors and simplify

4. Multiply: Factor numbers on numerator and denominator. Cancel common factors and use quotient rule.

5. Multiply:

6. = 3(a + b) Factor numerator Cancel common factors and use quotient rule

7. Divide: Dividing by a rational expression is the same as multiplying by its reciprocal. Change the division to a multiplication and invert the divisor. Factor numbers and use product rule

8. Cancel common factors Use quotient rule

9. Divide: Change the division to a multiplication and invert the divisor. Use quotient rule

10. Divide: Change the division to a multiplication and invert the divisor. Factor each expression

11. Cancel common factors x 2 + 7x – 18 xx +9-2 = (x + 9)(x – 2) x 2 – 17x + 30 xx -15-2 = (x – 15)(x – 2) 3x + 3 = 3(x + 1)

12. Divide: Change the division to a multiplication and invert the divisor. Factor common factors. Cancel common factors Factor all expressions

13. Divide: Change the division to a multiplication and invert the divisor. Factor all expressions. x 2 – 2xy + y 2 = x 2 – y 2 = (x + y) (x – y) xx - y (x – y) = (x – y) 2

14. Cancel common factors

15. Multiply: Factor common factors. Factor all expressions 2x 2 – 7x + 3 = 2xx - 1- 3 (2x – 1) (x – 3) x 2 + 2x – 3 = xx + 3 - 1 (x + 3) (x – 1)

16. Cancel common factors

17. Divide: Change division to multiplication. Factor all expressions 3r r +2s+5s 3r2r - s+5s 3r2r -s 3r2r +2s-s Cancel common factors

18. Divide: Change the division to a multiplication. Factor all expressions. Cancel common factors r 2 + 4r – 12 = r 2 + r – 6 = (r + 3) (r – 2) rr - 2+6 (r + 6) (r – 2)