# Ch 4: Rational Expressions and Functions

### About This Chapter

## Rational Expressions and Functions - Chapter Summary and Learning Objectives

A rational expression, also called a rational function, is a fraction with a polynomial as its numerator and denominator. The video lessons in this chapter will show you how to perform operations with rational expressions and give you practice problems to assess your skills. You'll learn to graph rational functions and analyze graphs of rational functions. At the end of this chapter, you should be able to:

- Add, subtract, multiply and divide rational expressions
- Solve a rational equation
- Understand and work with horizontal and vertical asymptotes
- Graph rational functions
- Analyze graphs of rational functions

Video | Objective |
---|---|

How to Multiply and Divide Rational Expressions | Learn to multiply and divide rational expressions. |

Multiplying and Dividing Rational Expressions: Practice Problems | Develop skill in multiplying and dividing rational expressions. |

How to Add and Subtract Rational Expressions | Learn to add and subtract rational expressions. |

Adding and Subtracting Rational Expressions: Practice Problems | Develop skill in adding and subtracting rational expressions. |

How to Solve a Rational Equation | Learn methods of solving a rational equation. |

Horizontal and Vertical Asymptotes | Gain an understanding of horizontal and vertical asymptotes. |

Graphing Rational Functions That Have Linear Polynomials | Graph rational functions that consist of two lineal polynomials. |

Graphing Rational Functions That Have Polynomials of Varying Degrees | Graph rational functions that consist of polynomials of varying degrees. |

Analyzing the Graph of a Rational Function: Asymptotes, Domain and Range | Identify asymptotes, domain and range algebraically and graphically. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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!

### 5. How to Solve a Rational Equation

A rational equation is one that contains fractions. Yes, we will be finding a common denominator that has 'x's. But no worries! Together we will use a process that will help us solve rational equations every time!

### 6. Horizontal and Vertical Asymptotes

No matter how hard you try to get to them, asymptotes remain out of reach. Learn about these invisible lines on graphs that show you places your equations just can't go.

### 7. Graphing Rational Functions That Have Linear Polynomials: Steps & Examples

Watch this video lesson to learn how you can graph rational functions with linear polynomials in just a few steps. Also learn what kinds of functions these are and what you need to look for to graph them.

### 8. Graphing Rational Functions That Have Polynomials of Various Degrees: Steps & Examples

Graphing rational functions is not as hard or as scary as it sounds. Sure, the functions may be big, but watch this video lesson and you will see that graphing these functions can actually be easy.

### 9. Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range

A rational function arises from the ratio of two polynomial expressions. The graphs of rational functions often have distinct characteristics. In this lesson, we look at how to analyze some of those characteristics.

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### Other Chapters

Other chapters within the Math 105: Precalculus Algebra course

- Mathematical Modeling
- Linear Equations & Inequalities
- Quadratic Functions
- Polynomial Functions of a Higher Degree
- Absolute Value Equations & Inequalities
- Complex Numbers
- Geometry Basics
- Functions Overview
- Function Operations
- Graph Symmetry
- Exponential and Logarithmic Functions
- Introduction to the Derivative
- Studying for Math 105