Rational Expressions A rational function is a function

Rational Expressions

A rational function is a function that can be expressed in the form where both f(x) and g(x) are polynomial functions. Examples of rational functions would be:

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

Simplify the following • 4

To multiply rational expressions: 1. Factor the numerator and denominator of each fraction. 2. Multiply the numerators and denominators of each fraction. 3. Divide by the common factors. 4. Write the answer in simplest form. 5

Example: Multiply . Factor the numerator and denominator of each fraction. Multiply. Divide by the common factors. Write the answer in simplest form. 6

To divide rational expressions: 1. Multiply the dividend by the reciprocal of the divisor. The reciprocal of is . 2. Multiply the numerators. Then multiply the denominators. 3. Divide by the common factors. 4. Write the answer in simplest form. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 7

Example: Divide . Multiply by the reciprocal of the divisor. Factor and multiply. Divide by the common factors. Simplest form Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 8