2. Section 6.1 Rational Expressions

3. Definition A rational expression is the ratio of two polynomials. Examples:

4. Evaluating Rational Expressions Evaluate for a) x = 0 b) x = 3 (a) (b) Cannot divide by 0 UNDEFINED. = 3 __ 0 Rational expression is undefined when its denominator equals to 0

5. Example Find all numbers for which is undefined Set denominator equal to 0 Factor LHS is undefined when its denominator equal to 0 Solve for x

6. Example Find all numbers for which is undefined Set denominator equal to 0 Factor LHS is undefined when its denominator equal to 0 Solve for x

7. Simplifying Rational Expressions Fundamental Property of Rational Expression A rational expression is in simplified form if its numerator and Its denominator have no common factors other than 1. To simplify a rational expression, we 1) Factor the numerator and denominator completely 2) Cancel common factors where A, B, C are polynomials We can multiply both numerator and denominator by the same polynomial. We can cancel out any common factors.

8. Example Simplify This expression is already in factored form Just cancel common factors 4 5 a3a3 1 b 1

9. Example Simplify Factor 1 2

10. Example Simplify Factor numerator and denominator completely 1 1

11. Example Simplify Factor out -1 in the numerator 1 1 = -1

12. Example Simplify 1 1 NO! No?

13. Example Simplify Multiply out 1 1

14. Example Simplify Factor 1 1 Difference of 2 squares

15. Example a) Evaluate the expression for m = 1 b) Evaluate the expression for m = -10 c) Find all values of m such that the expression is undefined d) Simplify the expression

16. More Examples