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### Course: Algebra (all content) > Unit 13

Lesson 1: Intro to rational expressions# Intro to rational expressions

Learn what rational expressions are and about the values for which they are undefined.

#### What you will learn in this lesson

This lesson will introduce you to rational expressions. You will learn how to determine when a rational expression is undefined and how to find its domain.

## What is a rational expression?

A $x$ , like $3{x}^{2}-6x-1$ .

**polynomial**is an expression that consists of a sum of terms containing integer powers ofA

**rational expression**is simply a*quotient*of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.These are examples of rational expressions:

Notice that the numerator can be a constant and that the polynomials can be of varying degrees and in multiple forms.

## Rational expressions and undefined values

Consider the rational expression $\frac{2x+3}{x-2}$ .

We can determine the value of this expression for particular $x$ -values. For example, let's evaluate the expression at ${x}={1}$ .

From this, we see that the value of the expression at ${x}={1}$ is ${-5}$ .

Now let's find the value of the expression at ${x}={2}$ .

An input of $2$ makes the denominator $0$ . Since division by $0$ is undefined, ${x}={2}$ is not a possible input for this expression!

## Domain of rational expressions

The

**domain**of any expression is the set of all possible input values.In the case of rational expressions, we can input any value except for those that make the denominator equal to $0$ (since division by $0$ is undefined).

In other words, the

**domain of a rational expression**includes all real numbers except for those that make its denominator zero.### Example: Finding the domain of $\frac{x+1}{(x-3)(x+4)}$

Let's find the zeros of the denominator and then restrict these values:

So we write that the domain is $x\ne 3,-4$ .

*all real numbers except*$\mathit{\text{3}}$ and $\mathit{\text{-4}}$ , or simply## Check your understanding

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