# Ch 1: Arithmetic with Rational Expressions

### About This Chapter

## Arithmetic with Rational Expressions - Chapter Summary

This chapter's lessons will help you understand operations with rational expressions. You'll learn what rational expressions are and how to work with them and be presented with practice problems. Our instructors will also explain how to solve rational equations and differentiate between direct and inverse variation problems. After watching all these lessons, you should be prepared to:

- Multiply, divide, add and subtract rational expressions
- Divide and take the reciprocal of rational equations
- Simplify complex rational expressions
- Solve equations of inverse and direct variation

You'll be guided through these short video lessons by our professional instructors. They know how to make learning enjoyable while explaining important concepts. They've created quizzes to accompany each lesson, allowing you to test your knowledge. If you need additional study on a key topic, a jump feature in the video timelines makes it quick to return to that portion of the lesson.

### 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. Division and Reciprocals of Rational Expressions

In this video lesson, you will learn how to divide and take the reciprocal of any rational expression. Learn the one easy step you take to be able to find your answer quickly and easily.

### 8. Simplifying Complex Rational Expressions

When it comes to fractions, things may seem to get really complicated and scary when you have a fraction on top of a fraction. But never fear, after watching this video lesson, you will be able to simplify these expressions like a pro.

### 9. Solving Equations of Direct Variation

In the real world, we come across a lot of problems that vary directly with each other. You will learn how to solve these types of direct variation problems in this video lesson.

### 10. Solving Equations of Inverse Variation

After watching this video lesson, you will be able to identify problems where you can use the formula for inverse variation to solve them. Learn what is involved and how easy they are to solve.

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### Other Chapters

Other chapters within the Accuplacer Math: Advanced Algebra and Functions Placement Test Study Guide course

- Factoring in Algebra
- Expanding Polynomials
- Manipulating Roots
- Working with Exponents & Exponential Expressions
- Solving & Graphing Linear Equations
- Quadratic Equations
- Calculating & Graphing Inequalities
- Solving Systems of Linear Equations
- Geometric Angles & Shapes
- Line Theorems
- Similarity & Congruency in Geometry
- Pythagorean Theorem
- Graphs of Algebraic Functions
- Understanding Exponential & Logarithmic Functions
- Trigonometric Functions & Equations
- Accuplacer Math: Advanced Algebra and Functions Placement Test Flashcards