1. Simplifying rational expressions

2. Simplest Form
A rational expression is in SIMPLEST FORM when its numerator and denominator are polynomials that have no common factors.
*Note: when simplifying we still need to remember holes.

3. Examples
Simplify the expression. State holes, vertical asymptotes, horizontal asymptotes, domain and range. 1.

4. Examples
Simplify the expression. State holes, vertical asymptotes, horizontal asymptotes, domain and range. 2.

5. Examples
Simplify the expression. State holes, vertical asymptotes, horizontal asymptotes, domain and range. 3.

6. Examples
Simplify the expression. State holes, vertical asymptotes, horizontal asymptotes, domain and range. 4.

7. Multiplying AND DIVIDING RATIONAL EXPRESSIONS

8. Review: Multiplying fractions

9. Multiplying Rational Functions
You multiply rational functions like you do every other fraction: STRAIGHT ACROSS
Steps:
Factor where needed
Multiply straight across
Simplify
(Don’t forget to write down your holes before you cancel out common factors)

10. Multiplying Rational Expressions

11. Multiplying Rational Expressions

12. Dividing Rational Expressions
Remember: Dividing by a fraction is the same thing as multiplying by the reciprocal. Flip the second fraction, multiply, then simplify. Keep  Change  Flip

13. Dividing Rational Expressions

14. Dividing Rational Expressions

15. Dividing Rational Expressions