# Ch 12: FTCE Middle Grades Math: Rational Expressions

### About This Chapter

## FTCE Middle Grades Mathematics: Rational Expressions - Chapter Summary

Use this chapter to review material on rational expressions to better prepare for the FTCE Middle Grades Mathematics Test. The instructors leading this chapter's video lessons will address the topics that may come up on this exam. The lessons in this chapter will cover information like:

- Multiplying and dividing rational expressions
- Adding and subtracting rational expressions
- Solving rational equations
- Division and reciprocals of rational expressions
- Strategies for simplifying complex rational expressions
- Analyzing the graphs of rational functions

In this chapter, you will get a handle on the concepts related to rational expressions that will appear on the FTCE Middle Grades Mathematics Test. After you've finished the lessons, you will be equipped with the information you need to answer rational expressions questions correctly. You can use our multiple-choice quizzes to test yourself on the types of questions that will appear on the exam.

### 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. 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.

### 3. 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!

### 4. 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.

### 5. 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.

### 6. 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

Other chapters within the FTCE Middle Grades Mathematics 5-9 (025): Practice & Study Guide course

- About the FTCE Middle Grades Mathematics Test
- FTCE Middle Grades Math: Mathematical Reasoning
- FTCE Middle Grades Math: Problem-Solving Strategies
- FTCE Middle Grades Math: The Real Number System
- FTCE Middle Grades Math: Fractions, Decimals & Percents
- FTCE Middle Grades Math: Ratios & Proportions
- FTCE Middle Grades Math: Factoring
- FTCE Middle Grades Math: Solving Word Problems
- FTCE Middle Grades Math: Exponents & Exponential Expressions
- FTCE Middle Grades Math: Basic Algebraic Expressions
- FTCE Middle Grades Math: Distributing in Algebra
- FTCE Middle Grades Math: Square Roots
- FTCE Middle Grades Math: Radical Expressions
- FTCE Middle Grades Math: Linear Equations
- FTCE Middle Grades Math: Systems of Linear Equations
- FTCE Middle Grades Math: Solving & Graphing Inequalities
- FTCE Middle Grades Math: Introduction to Functions
- FTCE Middle Grades Math: Graphing Functions
- FTCE Middle Grades Math: Quadratic Functions
- FTCE Middle Grades Math: Polynomial Functions
- FTCE Middle Grades Math: Summarizing Data
- FTCE Middle Grades Math: Charting Data
- FTCE Middle Grades Math: Sampling
- FTCE Middle Grades Math: Probability Distributions
- FTCE Middle Grades Math: Lines & Angles
- FTCE Middle Grades Math: Properties of Triangles
- FTCE Middle Grades Math: Similar & Congruent Triangle Proofs
- FTCE Middle Grades Math: Right Triangle Proofs
- FTCE Middle Grades Math: Quadrilaterals & Polygons
- FTCE Middle Grades Math: Area & Perimeter
- FTCE Middle Grades Math: Circles & Arc of a Circle
- FTCE Middle Grades Math: Coordinate Geometry
- FTCE Middle Grades Math: Transformations in Geometry
- FTCE Middle Grades Math: Principles of Measurement
- FTCE Middle Grades Math: Surface Area & Volume
- FTCE Middle Grades Math: Connecting Math Concepts
- FTCE Middle Grades Math: Instructional Strategies & Tools
- FTCE Middle Grades Math: Assessing Student Learning
- FTCE Middle Grades Mathematics 5-9 Flashcards