# Polynomial Division and Rational Expressions

### Topics

## Introduction to :

Evaluating a rational expression is exactly like evaluating any other expression. We substitute values for variables, do some arithmetic, and see what we find. It's usually much prettier than what we were previously dealing with, because we don't have all those ugly *x*'s and *y*'s hanging around by the end of it. However, with rational expressions, there's one thing to be careful of: we aren't allowed to put in values that make the denominator 0, because then we'd be dividing by 0 and the world would come crashing down.

Chicken Little thought things were bad when that acorn beaned him in the noggin. Watch out, Chicken Little. You'd better keep your eyes peeled for a whole other breed of ovoid.

### Sample Problem

Evaluate the rational expression at each given value of *x*.

1. *x* = -3.

We put in -3 for

xand find.

2. *x* = 0.

When we put in 0 for

x, we find.

Remember, it's fine if one of our variables equals 0, as long as the denominator doesn't. If we have nothing on bottom, we'll have real problems. We also won't be able to visit any public beaches.

3. *x* = 2.

We aren't allowed to do this, because we'll have (2)

^{2}– 4 = 0 in the denominator. See? We told you: no dividing by zero allowed. When, oh when, will we learn?

#### Exercise 1

Evaluate the rational expression for *x* = 1, or state that you can't evaluate the expression there because the denominator would be 0.

#### Exercise 2

Evaluate the rational expression for *x* = 0, or state that you can't evaluate the expression there because the denominator would be 0.

#### Exercise 3

Evaluate the rational expression for *x* = 2, or state that you can't evaluate the expression there because the denominator would be 0.

#### Exercise 4

Evaluate the rational expression for *x* = -2, or state that you can't evaluate the expression there because the denominator would be 0.

#### Exercise 5

Evaluate the rational expression for *x* = -3, or state that you can't evaluate the expression there because the denominator would be 0.