Solving Worksheets for Elementary Algebra

Confidence comes with  practice.

In Elementary Algebra we have learned how to solve four types of equations.  The ability to solve a variety of different types of equations takes time and practice to master.  Here are some extra exercises that you can use to hone your skills.

• [ Solving Linear Equations ]
• [ Solve Quadratic Equations by Factoring ]
• [ Solving Rational Equations ]
• [ Solving Radical Equations ]

If you are an instructor, please feel free to use these problems in your Beginning Algebra or Algebra 1 course. More supplementary material can be found on my Elementary Algebra Course page.


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Solving Rational Equations in Beginning Algebra

A thorough explanation for solving rational equations can be read for free in the Elementary Algebra textbook that is available on the Flat World Knowledge website:

[ Solving Rational Equations ] 

Also, you can click on the following rational equation to watch a video solution.

The basic steps for solving these equations are as follows:

Step 1: Factor all denominators and determine the LCD.

Step 2: Identify the restrictions. 

Step 3: Multiply both sides of the equation by the LCD. Distribute carefully and then simplify.

Step 4: Solve the resulting equation. 

Step 5: Check for extraneous solutions.

The complete solution is presented below:

Basically, we multiply both sides of the equation by the LCD as a means to clear the fractions.  This introduces the possibility for extraneous solutions and so we must check our answers.  Look for more Chapter 7 videos here.

[ Visually Searchable Algebra Problems ] 

Elementary Algebra (Ch. 7) Rational Expressions and Equations

Elementary Algebra is an open textbook that is available to read for free on the flatworld knowledge website. Chapter 7 gives an introduction to rational expressions (algebraic fractions) and rational equations.  In addition to word problems involving uniform motion there is a complete treatment of direct and inverse variation.

7.1 Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions
7.4 Complex Fractions
7.5 Solving Rational Equations
7.6 Applications of Rational Equations
7.7 Variation

You will find a complete review exercise section and a practice test.

7.8 Review Exercises and Sample Exam

Feel free to copy and paste the links found here and post them in your LMS. Links to all of the chapters can be found by clicking the Elementary Algebra course button at the top of this page.

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Video Examples of Rational Expressions and Equations

All of the "Try This!" problems in the open textbook Elementary Algebra have been solved and are available for free on YouTube. Click on the problems below to view the videos found in chapter 7.

Rational Expressions and Equations

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For further updates please feel free to circle the Elementary Algebra Google+ page for this book.
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Adding and Subtracting Rational Expressions

To simplify a rational expression:
Step 1:  Factor all denominators as a means to easily determine the LCD.
Step 2:  Multiply by the appropriate factors to obtain equivalent terms with a common denominator. 
Step 3:  Add or subtract the numerators and place the result over the common denominator. 
Step 4:  Simplify the resulting algebraic fraction.



A more involved example follows:

It is always a good idea to state the restrictions.  Remember that the restrictions are the values that produce zero in the denominator.

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