# Ch 8: Rational Expressions

### About This Chapter

## Rational Expressions

It can be challenging remembering math definitions. Wouldn't it be great if there were easy, rational explanations for some? Luckily, when it comes to rational expressions, there is indeed an easy, rational definition! Rational expressions are simply fractions that include variables in the numerator, denominator, or both, such as in 3*x*/*x*+3. In other words, rational expressions are fractions that contain polynomials. Easy, right?

In this series of lessons on rational expressions, you'll recall skills you've learned about how to treat fractions and discover how you can use similar applications with rational expressions. First, you'll learn how to simplify and solve rational expressions. Then, as you continue through the lessons, you'll learn to add, subtract, multiply, and divide them, identifying concepts like the least common multiple. You'll be able to apply and solidify your skills with these problems by going through several practice examples along the way.

Finally, you'll expand on your skills and learn how to solve rational equations, again going through plenty of practice problems to sharpen your skills. You'll even stretch your brain power to learn more abstract examples.

These lessons are taught by well-informed instructors. They also helped put together several short multiple-choice quizzes and a chapter exam so you can test your knowledge of rational expressions.

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. How to Solve a Rational Equation

Solving a rational equation involves finding the common denominator and multiplying all numbers by it, then simplifying and checking the answer. Explore rational equations and apply the steps involved to solve example problems.

### 6. Rational Equations: Practice Problems

Rational equations include fractions and a numerator and denominator with polynomials. Explore rational equation examples and practice problems and learn how to clear the fraction.

### 7. Practice Problem Set for Rational Expressions

If you'd like more opportunities to practice the concepts you've learned in this chapter, please download the following practice problem set. After you've completed the set, you can download the answer key to check your work and help your understanding. Please note that these documents are not permissible for use during your proctored exam.

### Earning College Credit

Did you know… We have over 220 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

### Other Chapters

Other chapters within the Math 101: College Algebra course

- Foundations of Linear Equations
- Matrices and Absolute Value
- Inequalities
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics
- Complex Numbers
- Exponents and Polynomials
- Functions
- Radical Expressions & Functions
- Exponentials and Logarithms
- Probability Mechanics
- Sequences and Series
- Studying for Math 101