Lesson 3

The same method can be applied to the addition and subtraction of rational expressions. As usual with rational expressions, non-permissible values must be considered. When adding and subtracting fractions, you can follow these steps:

• Ensure the two fractions have a common denominator.
• Add or subtract the numerator to find the resulting numerator. The resulting denominator is the same as the common denominator.
• If possible, simplify the fraction by dividing both the numerator and denominator by a common factor.

Try This 3

1. Simplify the following rational expression using the steps you discussed in Try This 2.
   
   
    
   
   
2. Do you think you completed question 1 correctly? Verify the sum by graphing the original expression  into Y1 = and your result into Y2 = on a graphing calculator. Go to the table and compare the values of Y1 and Y2 for each value of X. For the original expression and the result to be equivalent, the values of Y1 and Y2 must be the same. Ignore values of X that are non-permissible values. Note: As a refresher, you may wish to review question 4 of Try This 5 in Lesson 2.
3. Do you think the same procedure would work for a binomial in the denominator? Find out by evaluating the following rational expression.
   
   
    
   
4. Do you think you evaluated the expression correctly? Again, verify your results.

Save your responses in your course folder.

Share 2

With a partner, discuss any differences in your responses to Try This 3. 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. Refer to the graphing method of verifying your answers.
   1. What do you have to watch out for when using this method?
   2. Describe a different method you could use to verify your answers.
3. After verification, did you or your partner need to revise your calculations? Were you able to find your error(s)?

If required, save a record of your discussion in your course folder.