# Ch 18: Saxon Algebra 1: Simplifying Rational Expressions

### About This Chapter

## How It Works:

- Identify the lessons in the Saxon Simplifying Rational Expressions chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the simplifying rational expressions topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

## Students will learn:

- How to simplify complex rational expressions
- Operations with rational expressions
- Using factoring to simplify rational expressions
- How to rationalize denominators
- Complex fractions and how to simplify them

*Saxon is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. Simplifying Complex Rational Expressions

When it comes to fractions, things may seem to get really complicated and scary when you have a fraction on top of a fraction. But never fear, after watching this video lesson, you will be able to simplify these expressions like a pro.

### 2. How to Add and Subtract Rational Expressions

Adding and subtracting rational expressions brings everything you learned about fractions into the world of algebra. We will mix common denominators with factoring and FOILing.

### 3. Practice Adding and Subtracting Rational Expressions

Adding and subtracting rational expressions can feel daunting, especially when trying to find a common denominator. Let me show you the process I like to use. I think it will make adding and subtracting rational expressions more enjoyable!

### 4. How to Multiply and Divide Rational Expressions

Multiplying and dividing rational polynomial expressions is exactly like multiplying and dividing fractions. Like fractions, we will reduce. With polynomial expressions we use factoring and canceling. I also give you a little mnemonic to help you remember when you need a common denominator and when you don't.

### 5. Multiplying and Dividing Rational Expressions: Practice Problems

Let's continue looking at multiplying and dividing rational polynomials. In this lesson, we will look at a couple longer problems, while giving you some practice multiplying and dividing.

### 6. Simplifying Rational Expressions With Factoring

In this lesson, we will review rational expressions and factoring. Then, we will see how to use factoring to simplify rational expressions and actually put the process to use in an example.

### 7. Rationalizing Denominators in Radical Expressions

Radical expressions containing denominators are not simplified completely unless the denominator is free of radical symbols. This lesson will teach you how to remove a radical from the denominator of a fraction through a process called rationalizing the denominator.

### 8. How to Simplify Complex Fractions

When fractions are inside other fractions, it can get really confusing. In this lesson, we'll learn how to tackle complex fractions, using the tools math gives us to simplify and resolve the toughest ones.

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### Other Chapters

Other chapters within the Saxon Algebra 1 Homeschool: Online Textbook Help course

- Saxon Algebra 1: Operations With Whole Numbers
- Saxon Algebra 1: Fractions
- Saxon Algebra 1: Decimal Numbers
- Saxon Algebra 1: Graphs on the Coordinate Plane
- Saxon Algebra 1: Sets
- Saxon Algebra 1: Real Numbers
- Saxon Algebra 1: Number Theory
- Saxon Algebra 1: Properties of Real Numbers
- Saxon Algebra 1: Conversion by Unit Multipliers
- Saxon Algebra 1: Ratio, Rate & Proportion
- Saxon Algebra 1: Percent
- Saxon Algebra 1: Exponents
- Saxon Algebra 1: Roots
- Saxon Algebra 1: Probability
- Saxon Algebra 1: Statistics
- Saxon Algebra 1: Simplifying Expressions
- Saxon Algebra 1: Polynomials
- Saxon Algebra 1: Simplifying and Solving Equations
- Saxon Algebra 1: Linear Equations
- Saxon Algebra 1: Quadratic Equations
- Saxon Algebra 1: Other Types of Equations
- Saxon Algebra 1: Understanding Functions
- Saxon Algebra 1: Lines, Points, Segments, and Planes
- Saxon Algebra 1: Angles
- Saxon Algebra 1: Polygons
- Saxon Algebra 1: Circles
- Saxon Algebra 1: Triangles
- Saxon Algebra 1: Geometric Solids
- Saxon Algebra 1: Perimeter and Circumference
- Saxon Algebra 1: Area
- Saxon Algebra 1: Surface Area and Volume
- Saxon Algebra 1: Pythagorean Theorem