Operations with Rational Functions

Multiplication and Division

When we multiply or divide two rational expressions, the algebra that is used is simply an application of normal fraction manipulation.

The rules used to multiply and divide rational expressions are the same as those used to multiply and divide rational numbers.

Procedure To Multiply Rational Expressions

Step 1: Find the domain of definition

Step 2: Factor the numerators and denominators.

Step 3: Cancel all pairs of factors common to the numerators and denominators.

Step 4: Multiply the numerators, and then multiply the denominators.

Addition and Subtraction

To add or subtract two rational expressions we have to make sure that the terms have the same denominator.

Two cases will be discussed:

Case 1: If the denominators are the same, just add or subtract the numerators.

Step 1: Find the domain of definition

Step 2: Combine the numerators together.

Step 3: Put the sum or difference found in step 1 over the common denominator.

Step 4: Reduce to lowest terms if possible

Find out more about operations with rational functions by reading the explanation below.

Practice: Add, subtract, multiply and divide rational expressions to answer the exercise below.