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Multiply, Divide, Add, Subtract Rational Expressions

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More Lessons for Algebra
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A series of free, online Basic Algebra Lessons.

In this lesson, we will learn

  • how to multiply and divide rational expressions
  • how to add and subtract rational expressions
  • how to solve rational equations
The following diagrams give the steps to multiply, divide, add, and subtract Rational Expressions. Scroll down the page for examples and solutions.

Rational Expressions

Multiplying and Dividing Rational Expressions
Multiplying rational expressions is basically two simplifying problems put together.
When multiplying rationals, factor both numerators and denominators and identify equivalents of one to cancel.
Dividing rational expressions is the same as multiplying with one additional step: we take the reciprocal of the second fraction and change the division to multiplication.

How to multiply and divide rational expressions. Examples on how to multiply rational expressions when the numerators and denominators are monomials.



Examples on how to multiply rational expressions. Examples on how to divide rational expressions. Adding and Subtracting Rational Expressions
Adding and subtracting rational expressions is similar to adding fractions. When adding and subtracting rational expressions, we find a common denominator and then add the numerators. To find a common denominator, factor each first. This strategy is especially important when the denominators are trinomials.

How to add and subtract rational expression with and without like denominators. Examples of how to add and subtraction rational expressions with the the same denominators. Examples of how to add and subtraction rational expressions when the denominators are different. Examples of how to add and subtraction rational expressions when the denominators are different.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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