Determine the values for which a rational expression is undefinedEvaluate rational expressionsSimplify rational expressionsSimplify rational expressions with opposite factors

Before you get started, take this readiness quiz.

You are watching: Simplify the rational expression n^4-11n^2+30/n^4-7n^2+10

If you miss a problem, go back to the section listed and review the material.


In Chapter 1, we reviewed the properties of fractions and their operations. We introduced rational numbers, which are just fractions where the numerators and denominators are integers, and the denominator is not zero.

In this chapter, we will work with fractions whose numerators and denominators are polynomials. We call these rational expressions.


A rational expression is an expression of the form

*
*

*
*
*

*
*
*

Evaluate

*
*
*
*
Simplify.
*
This rational expression is undefined for x = 2.

*
*
*
*
for each value:

*
Simplify.
*
 when 
*
Simplify.
*
 when 
*
Simplify.
*
The expression is undefined.


Evaluate

*
Simplify using the Equivalent Fractions Property.
*
is simplified because there are no more common factors.


Simplify:

*
Simplify using the Equivalent Fractions Property.

See more: Convert Grams Per Centimeter Cubed To Kilograms Per Meter Cubed

*


*
would be like cancelling the 2’s in the fraction
*
Recognize that
*

Simplify:

*
Recognize the factors that are opposites.
*

Simplify:

*
, where p and q are polynomials and
*

Previous: Introduction