# Simplifying Rational Expressions

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What is a Rational Expression?
A rational expression is a fraction in which the numerator and/or the denominator are polynomials.

For example:

How to Simplify Rational Expressions?
In this lesson, we will look at simplifying rational expressions. A rational expression has been simplified or reduced to lowest terms if all common factors from the numerator and denominator have been canceled.
1. We first need to factor the polynomials
2. Cancel any common factors from the top and bottom of the rational expression.

Example:

Simplify each of the following rational expressions:

Solution:

Simplifying rational expressions - level 1
Example:
Simplify
(4x3 + 8x2)/2x

Simplifying rational expressions - level 2
Example:
Simplify
(7x2 + 28x)/(x2 + 8x + 16)
Simplifying rational expressions - level 3
Example:
Simplify
(4x2 + 4x + 1)/(2x3 + 11x2 + 5x)
How to write rational expressions in lowest terms?
Step 1: Factor them
Step 2: Cancel to write in lowest terms
Give the domain of the expressions
Examples:
Simplify
a) (x + 2)/(x2 + 5x + 6)
b) (x2 + 2x - 15)/(x2 + x - 12)
Rational Expressions: Writing in Lowest Terms
How to reduce a rational expression involving a cubic polynomial and a quadratic polynomial?
Examples:
Simplify
(x3 + 1)/(x2 + 7x + 6)

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