About This Chapter
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 3x/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
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. 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.
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.
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Other chapters within the Math 101: College Algebra course
- Foundations of Linear Equations
- Matrices and Absolute Value
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics
- Complex Numbers
- Exponents and Polynomials
- Radical Expressions & Functions
- Exponentials and Logarithms
- Probability Mechanics
- Sequences and Series
- Studying for Math 101