# Ch 7: Rational Expressions & Quadratic Equations

### About This Chapter

## Rational Expressions & Quadratic Equations - Chapter Summary

Use this chapter as a way to recall all the important details about rational expressions and quadratic equations. Our instructors have prepared this chapter specifically to give you a step-by-step recap of these topics. Our fast and fact-filled lessons will remind you about such concepts as asymptotes, rational polynomial expressions,quadratic equations, FOIL, and more. This chapter will help you describe rational functions and their expressions and dentify techniques for simplifying complex rational expressions. By the time you reach the end of the chapter, you will also know how to:

- Define multiplication and division strategies for rational expressions
- Examine steps for subtracting and adding rational expressions
- Explain ways to solve a rational equation
- Point out how to find the least common denominator in rational equations
- Establish the multiplication property of zero and the greatest common factor
- Show the implications of the quadratic formula for solving quadratic equations
- Determine what to do when quadratics are NOT in standard form
- Outline the use of substitution for solving quadratic equations

Many of our lessons are presented in the form of videos, but each video comes complete with a full lesson transcript. Although many users watch the video lessons first, lesson transcripts make for an easy-to-use study aid, especially when brushing up right before an exam. Our transcripts look like a professional set of notes, including large headers for major topics, examples of formulas, and the keywords are highlighted in either bold or italicized print.

### 1. Expressions of Rational Functions

In this video lesson, you will learn how to write a rational function given just the horizontal and vertical asymptotes. Learn how to write the asymptotes and where to write them in your function.

### 2. 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.

### 3. 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.

### 4. 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.

### 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. 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.

### 8. What is a Quadratic Equation? - Definition & Examples

You might be surprised to learn that quadratic equations are an important part of the world we live in. We sometimes even make use of them for our entertainment! Watch this video lesson to learn more about these equations.

### 9. Solving Quadratics: Assigning the Greatest Common Factor and Multiplication Property of Zero

When it comes to solving quadratics, we have at our disposal several methods. Watch this video lesson to learn one such method you can use to solve quadratics that don't have a constant term.

### 10. How to Use the Quadratic Formula to Solve a Quadratic Equation

When solving a quadratic equation by factoring doesn't work, the quadratic formula is here to save the day. Learn what it is and how to use it in this lesson.

### 11. How to Solve Quadratics That Are Not in Standard Form

It isn't always the case that your equation will be set up nicely for you to solve. In this lesson, learn how to factor or use the quadratic formula to solve quadratic equations, even when they are not in standard form.

### 12. Solving Quadratic Equations by Substitution

After watching this video lesson, you will be able to solve more complicated quadratic equations by the method of substitution. Learn how substitution makes your problem solving easier.

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### Other Chapters

Other chapters within the Alberta Education Diploma - Mathematics 30-2: Exam Prep & Study Guide course

- Problem Solving with Logic & Reasoning
- Number Systems & Factoring
- Set Theory & Venn Diagrams
- Probability & Uncertainty
- Permutations & Combinations in Probability
- Introduction to Relations & Functions
- Logarithmic & Exponential Operations
- Solving Problems with Polynomial Functions
- Sinusoidal Functions
- Alberta Education Diploma - Mathematics 30-2 Flashcards