A rational expression is similar to a fraction in several ways. The important difference is that a fraction is made of only numbers but a rational expression is made of polynomials, which can have both numbers and variables.

are examples of rational expressions.

In this unit, you will see that all the operations you have used with fractions also apply to rational expressions. In this lesson, you will learn how to simplify a rational expression, which is similar to reducing a fraction to its lowest terms.

To simplify a rational expression, you must know how to factor a polynomial. In this lesson, you will review two types of factoring. Be sure you review each type fully before you go on to the new material.
  • The first type of factoring you need to review when working with rational expressions is factoring using greatest common factor.
  • Read the following carefully, and talk to your teacher if you have any questions.

Factoring a polynomial using the greatest common factor (GCF):

You must determine the largest factor that is common to the three terms. This is the GCF.

5 is the largest number that can be factored out of 10, 25, and 5.

x2 is the highest power of x that can be factored out of x4, x3, and x2.

y is the highest power of y that can be factored out of y, y, and y2.

The greatest common factor for 10x4y + 25x3y − 5x2y2 is 5x2y.

Now, remove the greatest common factor to get the factored form 5x2y(2x2 + 5x - y).

Factoring a rational expression using the greatest common factor (GCF):

On the next page, you will practice factoring using greatest common factor. When you are comfortable with this type of factoring, continue your lesson. The second type of factoring will be reviewed later in the lesson.