Rational Expressions
 Home > Lessons > Rational Expressions Search | Updated May 22nd, 2021
Introduction

In this section, you will learn how to manipulate rational expressions. Here are the sections within this lesson:

 Prerequisite Knowledge To understand rational expressions (fractions) that also include variable expressions (letters), it is necessary to have a respectable understanding of fractions that do not contain variables. These lessons/videos may prove useful for those viewers who need to review some basic skills that involve fractions.       esson: Reducing Fractions       esson: Multiplying Fractions       esson: Dividing Fractions       esson: Adding and Subtracting Fractions Simplifying or Reducing Rational expressions are fractions. The word rational is based on the word ratio, which roughly means a comparison or union of two quantities.      When we are dealing with a ratio of two values or mathematical expressions, we can simplify the ratio if the numerator and the denominator contain a common factor. Let's look at this example.      It can be seen that the numerator and the denominator both contain the common factor of three. So, we can divide them both by three, like so.      The result of the division is this.      You can gain more detailed examples on how to reduce fractions by accessing this lesson.       esson: Reducing Fractions      The rational expression above is extremely basic. Let's look at a more complicated rational expression, like this one.      When we simplify this rational expression, we have to be careful how we simplify or reduce the fraction. We can only cancel factors, not sums or differences. In other words, we cannot reduce the 6 and the 12 above.      To reduce the ratio, we have to first factor the numerator and the denominator. If you are unfamiliar with factoring, please review our lesson of factoring before continuing on. However, we can factor the numerator, because both the terms there are divisible by 2. The denominator can be factored as a product of two binomials, like so.      Once factored, we can see now that the numerator and the denominator both contain the common factor, namely the x - 3.      This leaves us with a much more simplified rational expression.      Again, we have to be careful not to get overzealous with our canceling. Keep in mind that we can only cancel factors, not parts of sums and differences. Since we cannot divide the entire denominator by 2, we cannot reduce the rational expression by a factor of 2.
 Multiplying To understand how to multiply rational expressions that contain variables, first you have to know how to deal with fractions that contain no variables. Use this lesson if your skills with fractions need some help.       esson: Multiplying Fractions      This video will demonstrate how to multiply rational expressions.