# Ch 17: Saxon Algebra 2: 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 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:

- Simplifying complex rational expressions
- Basic operations with rational expressions
- Simplifying rational expressions with factoring
- Rationalizing denominators in rational expressions
- Addition of like terms
- Simplifying complex fractions
- Euler's Notation
- Simplifying complex numbers with multiple steps
- Conjugate of the denominator
- Simplifying complex numbers with multiplication and division

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

### 1. Simplifying Complex Rational Expressions

Simplifying complex rational expressions is done by rewriting the denominator and performing multiplication. Learn about complex rational expressions, how to rewrite and simplify the problem, and see how to solve several examples.

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

Rational polynomial expressions are fractions with a numerator and denominator that are polynomials and can be simplified as needed and act similarly to fractions when identifying a common denominator. Learn how rational expressions are added and subtracted by simplifying through several steps demonstrated in examples.

### 3. Practice Adding and Subtracting Rational Expressions

Rational expressions can be simplified and reduced using common numerators and denominators to be added and subtracted. Put the steps into action to add and subtract rational expressions and use FOIL to solve three practice problems.

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

Polynomial retinal expressions, being a fraction that contains a polynomial, are able to be divided and multiplied similarly to normal fractions. Explore the extra steps involved through three examples of how to factor, flip, slash, and multiply and divide rational expressions when needed.

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

The steps of multiplying or dividing rational polynomial expressions are to factor, flip (when dividing), slash or cancel, and multiply. Put these steps for multiplying and dividing rational expressions into action and master the concept by solving a series of example problems.

### 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

Rationalizing denominators is a process that is used to simplify radical expressions as much as possible. Discover when a radical expression is finished, and learn how to rationalize a denominator with one term or more than one term.

### 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.

### 9. Simplifying Complex Numbers: Addition of Like Terms

We will talk about complex numbers - their uses and their parts. Then, we will look at simplifying these types of numbers by adding like terms. Lastly, we will practice this process through various examples.

### 10. Simplifying Complex Numbers: Euler's Notation

Sometimes things in math get a little complex, especially when you're dealing with complex numbers. In this lesson, you'll learn how to simplify things using a nice way to represent complex numbers: Euler's Notation.

### 11. Simplifying Complex Numbers: Conjugate of the Denominator

Complex numbers can appear in a denominator and can be simplified by multiplying the numerator and denominator by the complex conjugate of the denominator. Follow the steps in this process to understand how to simplify complex numbers comfortably.

### 12. Simplifying Complex Numbers With Multiple Steps

Performing the basic operations with complex numbers isn't much different than doing so with polynomials. In this lesson, we'll go over what exactly you must know about complex numbers, including some key facts that'll help you perform these operations.

### 13. Simplifying Complex Numbers With Multiplication & Division

In this lesson, we'll review the definition of complex numbers. With the aid of illustrations, we'll also look at the steps involved in simplifying complex numbers with multiplication and division.

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### Other Chapters

Other chapters within the Saxon Algebra 2 Homeschool: Online Textbook Help course

- Saxon Algebra 2: Decimal Numbers
- Saxon Algebra 2: Graphs on the Coordinate Plane
- Saxon Algebra 2: Sets
- Saxon Algebra 2: Real Numbers
- Saxon Algebra 2: Complex Numbers
- Saxon Algebra 2: Conversion by Unit Multipliers
- Saxon Algebra 2: Ratio & Proportion
- Saxon Algebra 2: Percent
- Saxon Algebra 2: Rate
- Saxon Algebra 2: Exponents
- Saxon Algebra 2: Exponents on a Scientific Calculator
- Saxon Algebra 2: Roots
- Saxon Algebra 2: Probability
- Saxon Algebra 2: Statistics
- Saxon Algebra 2: Simplifying Expressions
- Saxon Algebra 2: Polynomials
- Saxon Algebra 2: Simplifying and Solving Equations
- Saxon Algebra 2: Linear Equations
- Saxon Algebra 2: Solving Linear Equations
- Saxon Algebra 2: Quadratic Equations
- Saxon Algebra 2: Other Types of Equations
- Saxon Algebra 2: Understanding Functions
- Saxon Algebra 2: Manipulating and Evaluating Functions
- Saxon Algebra 2: Trigonometry
- Saxon Algebra 2: Logarithms
- Saxon Algebra 2: Lines, Points, Segments, and Planes
- Saxon Algebra 2: Angles
- Saxon Algebra 2: Polygons
- Saxon Algebra 2: Circles
- Saxon Algebra 2: Triangles
- Saxon Algebra 2: Geometric Solids
- Saxon Algebra 2: Perimeter and Circumference
- Saxon Algebra 2: Area
- Saxon Algebra 2: Surface Area and Volume
- Saxon Algebra 2: Constructions
- Saxon Algebra 2: Postulates & Pythagorean Theorem
- Saxon Algebra 2: Proofs