Table of Contents |
When first learning how to simplify rational expressions (or algebraic fractions), it can be very helpful to review how we simplify numeric fractions (containing no variables). This is because the thought process is the same. The only difference is that we have variables and algebraic factors to consider when simplifying rational expressions.
EXAMPLE
Simplify the fraction .Break numerator and denominator into prime factors | |
Two factors of 2 cancel | |
Simplify | |
Evaluate | |
Our simplified fraction |
The same principle applies to simplifying rational expressions. We look for common factors in both the numerator and denominator and cancel them. The only tricky there here is identifying those common factors, and in some cases, not confusing them for terms.
EXAMPLE
Simplify the expression .The factors cancel | |
Simplify | |
Our solution |
Simplifying rational expressions would be so easy if all rational expressions were written in factored form. Unfortunately, this isn't the case. However, we may be able to write the numerator and denominator as factors, or at least factor out a few common factors, in order to cancel and simplify the expression.
EXAMPLE
Simplify the expression .Factor out 2 in the numerator and 4 in the denominator | |
Cancel 2 out of both numerator and denominator | |
Simplify | |
Distribute denominator | |
Our simplified fraction |
Let's work through a final example, in which factoring the expressions in the numerator and denominator will lead to common factors:
EXAMPLE
Simplify .Factor out 6 in the numerator and 4 in the denominator | |
6/4 simplifies to 3/2 | |
Factor the numerator and denominator | |
The factors cancel | |
Distribute both numerator and denominator | |
Our simplified function |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License