# Ch 13: Algebra II: Rational Expressions

### About This Chapter

## Algebra II: Rational Expressions - Chapter Summary and Learning Objectives

The lessons contained in the Algebra II chapter demonstrate how to add, subtract, multiply and divide rational expressions. You'll also learn how to solve rational equations and graph reflections. Use concise and easy-to-understand video lessons that provide several sets of practice problems to test your understanding. When you finish this chapter, you should have an understanding of:

- Rational expressions
- Rational equations
- Reciprocals
- Complex rational expressions
- Direction variation
- Graphing reflections
- Least common denominators

Video | Objective |
---|---|

How to Multiply and Divide Rational Expressions | Understand the steps needed to multiply and divide rational expressions. |

Multiplying and Dividing Rational Expressions: Practice Problems | Practice multiplying and dividing rational expressions through sample questions. |

How to Add and Subtract Rational Expressions | Learn how to add and subtract rational expressions. |

Practice Adding and Subtracting Rational Expressions | Practice adding and subtracting rational expressions with example equations. |

How to Solve a Rational Equation | Know how to solve several different types of rational equations. |

Rational Equations: Practice Problems | Practice answering problems with different rational equations. |

Division and Reciprocals of Radical Expressions | Comprehend how to find the reciprocal of a rational expression through division. |

Simplifying Complex Rational Expressions | Provide a definition of complex rational expressions and understand how to simplify these expressions. |

Solving Equations of Direct Variation | Find the equation of direct variation and solve applied problems that involve direct variation. |

How to Graph Reflections Across Axes, the Origin and Line Y=X | Graph reflections across the y-axis, x-axis, origin and the line y=x. |

Solving Rational Equations and Finding the Least Common Denominator | Understand how to find the least common denominator of rational expressions and use this to solve equations. |

### 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. How to Graph Reflections Across Axes, the Origin, and Line y=x

A graph can be reflected in three ways - across the axes, the origin and the line y = x. There are specific rules to perform each reflection. This lesson will describe those rules and show you how to perform these reflections.

### 11. Solving Rational Equations and Finding the Least Common Denominator

When solving rational equations, just like with any other fractions, you must first find the least common denominator. This lesson will show you how to find the least common denominator and also solve the rational equations.

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### Other Chapters

Other chapters within the Algebra II: High School course

- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Teacher Resources for High School Algebra II