1. Lesson 3

1.6. Explore 2

Mathematics 20-1 Module 6

Module 6: Rational Expressions

 
Adding and Subtracting Rational Expressions with Common Denominators

 

To add or subtract fractions with a common denominator, you must add or subtract the numerators and write the result over the denominator. Examples of how rational numbers are added and subtracted are shown below.

 

Example 1

 

Evaluate the following expressions.



Solution



The same method can be applied to the addition and subtraction of rational expressions. As usual with rational expressions, you must be sure to note the non-permissible values.

 

Try This 2
  1. Evaluate the following rational expressions and state the non-permissible values. Use the same pattern shown in Example 1.







  2. Verify your results by

    1. graphing the original expression and your result into a graphing calculator

    2. substituting a known value of the variable into the original expression and the result

course folder Save your work in your course folder.

 

Share 1

 

Compare your answers to Try This 2 with a partner. Discuss any differences in your responses. Make any necessary revisions once a consensus has been reached.

  1. Describe a procedure that can be followed to determine the sum or difference, in simplest form, of rational expressions with the same denominator.

  2. The sum in 1.c. is equal to a constant. What did you have to do to simplify the expression to a constant?

  3. Refer to the two methods of verifying your answers in Try This 2 question 2.

    1. What do you have to watch out for when using each of these methods?

    2. Which method do you prefer and why?

  4. How would you add or subtract rational expressions with unlike denominators?

course folder Save your work in your course folder.


textbook

Work through “Example 1” on page 333 in the textbook. You will see three examples that are similar to those you investigated in Try This 2. As you work through the examples, you may find some things you might have overlooked in Share 1. Make any necessary revisions to your Share 1 responses. Focus on the following points as you work through “Example 1:”

  • In “Example 1.a.,” what would happen if brackets were not placed around “a – 1”? How do you know when brackets are necessary and when they are not?

  • “Example 1.b.” is similar to Try This 2 question 1.c. What is the important step here for simplifying the answer to a constant?

  • In “Example 1.c.,” why is there a non-permissible value, x ≠ 2, even though there is no denominator in the final result?
Self-Check 1

 

This is a play button that opens Adding and Subtracting Rational Expressions Self-Check: Common Denominators.

Complete Adding and Subtracting Rational Expressions Self-Check: Common Denominators.