1. Operations on Rational Expressions MULTIPLY/DIVIDE/SIMPLIFY

2. Rational expressions are fractions in which the numerator and denominator are polynomials and the denominator does not equal zero. Example: Simplify, x – 3  0, x  3

3. 1. FACTOR the numerator and denominator of each fraction. 3. Multiply what is left in the numerators and denominators of each fraction, and simplify. **Most of the time, we will leave both the numerator and denominator in factored form! To multiply rational expressions: 2. Cancel out any common factors FIRST.

4. Factor the numerator and denominator of each fraction. MultiplyExample: Multiply and simplify. Cancel out any common factors.

5. 1. Multiply the dividend by the reciprocal of the divisor. The reciprocal of is. **Same process as multiplication, except you have to flip the second expression first! To divide rational expressions:

6. Example: Divide Multiply by the reciprocal of the divisor. Multiply and simplify. Factor the numerator and denominator of each fraction.