# Ch 12: Chapter 12: Rational Expressions and Functions

### About This Chapter

## How It Works:

- Identify the lessons in the Prentice Hall Rational Expressions and Functions chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the algebra 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 about:

- Graphing rational functions
- Working with vertical and horizontal asymptotes
- Dividing and multiplying rational expressions
- Dividing polynomials with long division
- Adding and subtracting rational expressions
- Solving rational equations
- The fundamental counting principle
- Calculating a permutation
- Math combinations

*Prentice Hall is a registered trademark of Pearson Education, which is not affiliated with Study.com.*

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. How to Divide Polynomials with Long Division

Arithmetic long division and polynomial long division are very similar. Yes, it's a long process, but once you have the rhythm you will get every problem correct!

### 6. 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.

### 7. 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!

### 8. 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!

### 9. Rational Equations: Practice Problems

Mario and Bill own a local carwash and have several complex tasks that they must use rational equations to solve for an answer. Enjoy learning how they solve these equations to help them with some of their day-to-day tasks.

### 10. How to Use the Fundamental Counting Principle

There are many situations in which you will have to make several decisions simultaneously. The fundamental counting principle will help you determine how many different possible outcomes there are when you have to make multiple simultaneous decisions.

### 11. How to Calculate a Permutation

A permutation is a method used to calculate the total outcomes of a situation where order is important. In this lesson, John will use permutations to help him organize the cards in his poker hand and order a pizza.

### 12. Math Combinations: Formula and Example Problems

Combinations are an arrangement of objects where order does not matter. In this lesson, the coach of the Wildcats basketball team uses combinations to help his team prepare for the upcoming season.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Prentice Hall Algebra 1: Online Textbook Help course

- Chapter 1: Variables, Function Patterns, and Graphs
- Chapter 2: Rational Numbers
- Chapter 3: Solving Equations
- Chapter 4: Solving Inequalities
- Chapter 5: Graphs and Functions
- Chapter 6: Linear Equations and Their Graphs
- Chapter 7: Systems of Equations and Inequalities
- Chapter 8: Exponents and Exponential Functions
- Chapter 9: Polynomials and Factoring
- Chapter 10: Quadratic Equations and Functions
- Chapter 11: Radical Expressions and Equations