1. 9.1 Simplifying Rational Expressions Objectives 1. simplify rational expressions. 2. simplify complex fractions.

2. Rational Expression A function where the numerator and denominator are polynomials Excluded values are where the denominator equals zero (since a fraction cannot have a denominator of zero) To find excluded values, set the denominator equal to zero and solve for the variable

3. To simplify: Factor all polynomials, WATCH FOR GCF Cancel like factors in the numerator and denominator NEVER CANCEL ON EITHER SIDE OF A + OR - SIGN

4. Example: Simplify using exponent rules Example: Simplify by factoring

5. How do I find the values that make an expression undefined? Completely factor the original denominator.

6. The expression is undefined when: a= 0, 2, and -2 and b= 0. Factor the denominator

7. Lets go through another example. Factor out the GCF Next

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10. Multiplying Rational Expressions Factor ALL polynomials Cancel like terms, 1 from the numerator and 1 from the denominator (they do not have to be in the same fraction) Multiply together all remaining terms

11. Example 1: Example 2:

12. Dividing Rational Expressions Flip the second fraction and change the division sign to a multiplication sign Factor and cancel Side Note: If the numerator and denominator are opposites they will reduce to -1 when cancelled

13. Example 1: Example 2:

14. Complex fractions Fraction in a fraction Flip the denominator and change to multiplication Factor and cancel