# Ch 7: Common Core HS Algebra: Rational and Radical Expressions and Equations

### About This Chapter

**Standard:** Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. (CCSS.Math.Content.HSA-APR.D.7)

**Standard:** Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. (CCSS.Math.Content.HSA-REI.A.2)

## About This Chapter

Students who have mastered these standards are able to add, subtract, multiply and divide rational equations. They can also explain the reasoning behind solving radical and rational equations, as well as provide examples of solutions for radical and rational equations.

Lessons in this standard cover concepts such as:

- Solving rational equations
- Finding the answers to radical equations
- Explaining the difference between rational and radical equations

Students demonstrate mastery of these standards by expertly using the five steps for solving a rational equation. Mastery of these standards supports their future understanding of expressions containing nth roots, along with equations that have fractions with unknown variables.

### How to Use These Lessons in Your Classroom

Here are some tips for how to use the lessons to support instruction in these standards:

#### Adding, Subtracting, Multiplying and Dividing Rational Equations Lessons

Develop a worksheet and pass it out to your students. Have the students watch the video lessons regarding subtracting, dividing, multiplying and adding rational equations. Instruct the students to fill out the worksheet for homework. Spend the next day explaining how to correctly answer each question.

#### Solving Rational Equations Lessons

Create and pass out a worksheet that is made up entirely of rational equations. Show the video lesson 'How to Solve a Rational Equation' and instruct the students to complete the worksheet while watching the video. Call on students to come up to the chalkboard to work out equations from the worksheet. Ask them to explain the steps they're taking to find their answers.

#### Solving Radical Equations Lessons

Require your class to watch the 'How to Solve a Radical Equation' video lesson. As a class, take our video lesson's supplementary quiz. Spend time with the class watching the follow up video lesson called 'Radical Equations: Practice Problem.' Provide your students step-by-step guidance on how to answer this lesson's questions. Have your students spend the last part of the class taking the quiz for the practice problems lesson.

### 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. Solving Radical Equations: Steps and Examples

Solving radical equations is not any more difficult than solving other algebraic equations. This lesson will show you how to solve equations containing a square root and give some real-world examples.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Common Core Math - Algebra: High School Standards course

- Common Core HS Algebra: Algebraic Expressions
- Common Core HS Algebra: Linear Equations
- Common Core HS Algebra: Linear Inequalities
- Common Core HS Algebra: Quadratics
- Common Core HS Algebra: Exponents and Exponential Functions
- Common Core HS Algebra: Polynomials
- Common Core HS Algebra: Systems of Equations
- Common Core HS Algebra: Matrices
- Common Core HS Algebra: Sequences and Series
- Understanding Common Core Standards