Introduction: A rational ex pression is a fraction
with polynomials as the numerator and
denominator . In this activity you will learn how to simplify a rational
expression . If you fol low the
procedure of this activity you will simplify correctly every time.
First, let’s quickly look at how NOT to simplify. Here is a typical error of
many students who do not
understand what it means to simplify.
by "canceling" the 2x2
in the top with the 2x2
in the bottom.
One way to see this is incorrect is to substiute a number in place of x and see
that you do not get the
same result. For example let x = 1, then 
Now, let’s look at the correct, fool-proof way to
simplify. We will use lots of parentheses as they are
free, they can be thrown away when no longer needed and they don’t pollute the
environment! Here
are the steps to reducing a rational expression.
1. Give the numerator and the denominator each its own
set of parentheses.
2. Factor the numerator and the denominator and give each
factor (including monomial and constant factors!) its own
set of parentheses.
3. Identify and then remove ("cancel") parentheses
(factors)
in the numerator and the denominator that are identical.
4. (Optional) Remove any unnecessary parentheses.
Here are two (2) more examples.
Task 1. Use the method described above to simplify the
following expressions
Task 2. Simplify the right side of the equation .
Verify your result by comparing either graphing calculator tables
or graphs for the original function with that of the simplified form.
Task 3. Try to explain the following.
A student tries to reduce the expression 
as
follows:
Next, the student substitutes 3 for x in the original
expression, with the result:
Now, the student substitutes 3 for x in the reduced
expression, with the result:
The student then concludes that the result
is correct.
Try to explain either why the student is correct or why the student is
incorrect.
