# Ch 11: ELM Test - Algebra: Rational Expressions

### About This Chapter

## ELM Algebra: Rational Expressions - Chapter Summary

Review the concepts needed for the ELM exam with this online course. Video lessons in this chapter cover the following topics:

- How to Add and Subtract Rational Expressions
- Practice Adding and Subtracting Rational Expressions
- How to Multiply and Divide Rational Expressions
- Multiplying and Dividing Rational Expressions: Practice Problems
- How to Solve a Rational Equation
- Rational Equations: Practice Problems
- Solving Rational Equations with Literal Coefficients
- Solving Problems using Rational Equations
- Finding Constant and Average Rates
- Solving Problems using Rates

Watch our online videos, which break these concepts down into easy-to-understand parts and provide examples to help you practice. Then test your knowledge with a quiz!

### ELM Objectives

The ELM is a math proficiency exam required for all incoming students to schools in the California State University system. You can learn more about the topics on the ELM here.

The lessons in this chapter cover the Rational Expressions topic in the Algebra portion of the ELM. Algebra comprises approximately 35% of the entire exam. This chapter best addresses the 'evaluate and interpret algebraic expressions' objective. Additional chapters cover other essential objectives, such as:

- Use properties of exponents
- Perform polynomial arithmetic
- Solve linear equations
- Solve systems of linear equations in two unknowns
- Find and use slopes and intercepts of lines

### 1. 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.

### 2. 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!

### 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 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. Solving Rational Equations with Literal Coefficients

Watch this video lesson and be amazed at how you can solve a rational equation with numbers and letters in it. Learn how to solve rational equations with literal coefficients, and you will learn how to solve any rational equation you come across!

### 8. Solving Problems Using Rational Equations

Follow the steps you will learn in this video lesson to help you solve rational equation problems. See how the process turns what looks like a huge problem into a much simpler and easier to manage problem.

### 9. Finding Constant and Average Rates

Watch this video lesson to learn the differences between constant and average rates. You will learn the steps you need to take to find them and get two great visuals you can keep in mind to help you solve these rate problems.

### 10. Solving Problems Using Rates

In this video lesson, learn how to set up rate problems so you can easily solve them. You will become familiar with the rate formula and you will see how easy it is to use.

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### Other Chapters

Other chapters within the ELM: CSU Math Study Guide course

- ELM Test - Numbers and Data: Basic Arithmetic Calculations
- ELM Test - Numbers and Data: Rational Numbers
- ELM Test - Numbers and Data: Decimals and Percents
- ELM Test - Numbers and Data: Irrational Numbers
- ELM Test - Numbers and Data: Data & Statistics
- ELM Test - Algebra: Basic Expressions
- ELM Test - Algebra: Exponents
- ELM Test - Algebra: Linear Equations & Inequalities
- ELM Test - Algebra: Absolute Value Equations & Inequalities
- ELM Test - Algebra: Polynomials
- ELM Test - Geometry: Perimeter, Area & Volume
- ELM Test - Geometry: Properties of Objects
- ELM Test - Geometry: Graphing Basics
- ELM Test - Geometry: Graphing Functions
- About the ELM Test
- ELM Flashcards