Lesson 1

In Try This 1 you found that by applying a series of mathematical operations to a number, you end up with a number that is two less than the original number. The following statement summarizes this observation.

 

 

The expression is equivalent to the expression x − 2  for all values of x, except when x = −2.

 

In Try This 4 you will use the same principles demonstrated in the previous example to confirm this result.

 

Try This 4

1. Consider the rational expression Show that this expression simplifies to x − 2.
   
   
   
   
2. Simplify the rational expression State any non-permissible values.

 Save your responses in your course folder.

 

Share 2

 

Part A: Discussion

 

Discuss the following questions with a partner. Record your responses.

1. What are some key differences between simplifying rational numbers and simplifying rational expressions?
   
   
2. Why is it necessary to include the non-permissible value(s) with the simplified form even though this form may not have a denominator?
   
   
3. Based on your answer to question 2, when should you identify non-permissible values?

Part B: Calculator Verification

 

You can use your graphing calculator to verify that two expressions are equivalent. Follow the steps outlined below for each of three rational expressions and their simplified forms. Use the following rational expressions and the equivalent expressions you obtained in Try This 3 question 1:

1. 
   
   
2. 
   
   
3. 

Step 1: Input the rational expression into Y1 of the Y= editor.

 

Step 2: Input the other rational expression into Y2 of the Y= editor. If you have the option to do so, set the graph to a different thickness.

 

Step 3: Graph the expressions. If the first expression graphs over the second expression, you have confirmed that the expressions are the same.

 

Discuss the following questions in relation to the calculator verification procedure.

4. The graphs should appear to be identical. In fact, they are not. Can you identify where the two graphs are not identical and give an explanation as to why this is the case?
   
   
5. How can you recognize when two rational expressions that appear to be identical are, in fact, not identical?

Save your responses in your course folder.

 

Your teacher may wish to check your answers to ensure you have a good grasp of the material learned so far.