About This Chapter
ASSET Intermediate Algebra: Simplifying Rational Expressions - Chapter Summary
Explore the process of simplifying and performing operations on rational expressions before you take the ASSET Intermediate Algebra Test. Colorful video lessons reinforce your knowledge of the steps for solving equations, including finding a common denominator, factoring, simplifying a numerator and rewriting fractions. When you reach the end of the chapter, you should be able to confidently:
- Add, subtract, divide and multiply rational expressions, and correctly solve practice problems
- Define and find the answers to rational equations
- Recognize horizontal and vertical asymptotes
- Graph a rational function and identify domain and range
Filled with brief lessons that offer both visual appeal and in-depth explanations, this chapter was developed by experts. Transcripts are included for those who prefer to learn and absorb information by reading. This is an online program of study, so you can take the chapter anywhere throughout your day. Submit your questions as they arise by visiting the Dashboard and using the ask-an-expert function. When you've watched all of the lessons, make sure to take the corresponding quizzes.
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 within the ASSET Intermediate Algebra Test: Practice & Study Guide course
- ASSET Intermediate Algebra: Graphing Basics
- ASSET Intermediate Algebra: Factoring Polynomials
- ASSET Intermediate Algebra: Linear Equations
- ASSET Intermediate Algebra: Simplifying Radical Expressions
- ASSET Intermediate Algebra: Slope & Distance Formulas
- ASSET Intermediate Algebra: Linear Inequalities
- ASSET Intermediate Algebra Test Flashcards