# Ch 17: High School Algebra: Rational Expressions

### About This Chapter

## Rational Expressions - Chapter Summary and Learning Objectives

Our instructor's initial goal in these lessons is to train you how to multiply, divide, subtract and add rational expressions. Following the basic rational expressions lessons, you will be provided with lessons that allow you to practice basic concepts. By the end of this chapter, you should also know how to:

- Solve rational equations
- Simplify and define complex rational expressions
- Find the answer to problems that include inverse variation or direct variation
- Determine the reciprocal of a rational expression

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

How to Multiply and Divide Rational Expressions | Demonstrate multiplying and dividing rational expressions. |

Multiplying and Dividing Rational Expressions: Practice Problems | Get practice dividing and multiplying rational expressions. |

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

Practice Adding and Subtracting Rational Expressions | Get practice subtracting and adding rational expressions. |

How to Solve a Rational Equation | Explain how to solve a rational equation. |

Rational Equations: Practice Problems | Receive practice solving rational equations. |

Division and Reciprocals of Radical Expressions | Explain how to find the reciprocal of a rational expression. Then divide rational expressions and simplify. |

Simplifying Complex Rational Expressions | Define complex rational expression. Explain how to simplify complex rational expressions. |

Solving Equations of Direct Variation | Explain how to find an equation of direct variation given a pair of values of the variables. Demonstrate how to solve applied problems involving direct variation. |

Solving Equations of Inverse Variation | Explain how to find an equation of inverse variation given a pair of values of the variables. Demonstrate how to solve applied problems involving inverse variation. |

### 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 Algebra I: High School course

- High School Algebra: Solving Math Word Problems
- High School Algebra: Percent Notation
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Properties of Exponents
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Algebraic Distribution
- High School Algebra: Properties of Functions
- High School Algebra: Working With Inequalities
- High School Algebra: Linear Equations
- High School Algebra: Factoring
- High School Algebra: Quadratic Equations
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Data, Statistics, and Probability
- Teacher Resources for High School Algebra