1. 10/24/2015 1 Simplifying, Multiplying and Dividing Rational Expressions

2. 10/24/2015 2 Simplifying Rational Expressions Let a, b, and c be nonzero real numbers (or variable expressions). Then,

3. 10/24/2015 3 Example: Simplify Factor the numerator and denominator Cancel common factors Rewrite the simplified expression

4. 10/24/2015 4 Example: Simplify

5. 10/24/2015 5 Multiplying Rational Expressions with Monomials Simplify as much as possible Multiply numerators Multiply denominators Simplify Rewrite the simplified expression

6. 10/24/2015 6 Example: 2 5 3

7. 10/24/2015 7 Multiplying Rational Expressions with polynomials Factor the numerators and denominators of each rational expression Simplify by dividing out common factors Multiply Rewrite in simplified form (no parentheses or negative exponents)

8. 10/24/2015 8 Example:

9. 10/24/2015 9 Dividing Rational Expressions Rewrite as a multiplication problem (Multiply the first by the reciprocal of the second.) Factor numerators and denominators Simplify Multiply Rewrite the answers in simplified form

10. 10/24/2015 10 Example:

11. 10/24/2015 11 Multiplying or Dividing Rational Expressions by Polynomials Treat the denominator of the polynomial expression as 1. Factor each numerator and denominator Multiply/”Divide” Rewrite in simplified form

12. 10/24/2015 12 Example

13. 10/24/2015 13 Assignment Page 558 #16-49