# Ch 5: Calculating Rational Expressions

### About This Chapter

## Calculating Rational Expressions - Chapter Summary and Learning Objectives

Within your algebra study, you'll want to become adept at performing all basic operations on rational expressions, from adding to dividing. This chapter of brief video lessons can help you out with that, in addition to guiding you in solving rational equations, simplifying complex rational expressions and solving equations of direct variation. By the time you're finished, you should be comfortable with the following:

- Reciprocals of rational expressions
- Graphing reflections across axes, the origin and line Y=X
- Solving rational equations
- Finding the least common denominator

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

How to Multiply and Divide Rational Expressions | Learn about the major role that reducing plays in this procedure. |

Multiplying and Dividing Rational Expressions: Practice Problems | Practice the steps for multiplying and dividing rational polynomials. |

How to Add and Subtract Rational Expressions | Use your knowledge of fractions, factoring and FOIL in this lesson's exercises. |

Practice Adding and Subtracting Rational Expressions | Discover a handy method for adding and subtracting rational expressions and a trick for remembering when a common denominator is needed. |

How to Solve a Rational Equation | Learn to be on the lookout for extraneous solutions and practice the necessary steps for solving rational equations. |

Rational Equations: Practice Problems | Find out why clearing an equation of fractions is crucial and the steps that should then follow in solving rational equations. |

Division and Reciprocals of Rational Expressions | Review rational numbers, rational expressions and reciprocals. |

Simplifying Complex Rational Expressions | Explore how to simplify, flip a fraction, look for common terms and multiply for solutions. |

Solving Equations of Direct Variation | Learn how to use the formula for direct variation. |

How to Graph Reflections Across Axes, the Origin, and Line Y=X | Learn the rules of reflections and strategies for drawing reflections. |

Solving Rational Equations and Finding the Least Common Denominator | Take a look at strategies for finding the least common denominator, writing your expressions and solving equations for x. |

### 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 2 and Trig Textbook course

- Identifying Real Numbers
- Complex Numbers
- Absolute Value Review
- Solving Algebraic Expressions & Equations
- Working with Linear Equations
- Solving & Graphing Inequalities
- Graphing & Working with Trigonometric Functions
- Graph Symmetry
- Graphing with Functions
- Solving Linear Equations
- Calculating & Graphing Polynomials
- Calculating & Simplifying Exponential Expressions
- Square Roots & Radical Expressions
- Quadratic Equations & Formulas
- Factoring & Graphing Quadratic Equations
- Conic Sections: Ellipses, Circles, Hyperbolas & Parabolas
- Vectors, Matrices and Determinants
- Exponential Functions & Logarithmic Functions
- Arithmetic & Geometric Sequences & Series
- Calculating & Presenting Statistics
- Combinatorics & Probability
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Equations
- Trigonometric Identities
- Circles, Angles & Circular Arcs