Math 45

Sample 2nd Midterm

Problem 2

Method 2

Dr. Wilson

2. Simplify

Method 2. Multiply the top and bottom by a common denominator.

The common denominator for both the top and bottom is 3(x + 2). Multiply the top and bottom of the big fraction by this common denominator.

We put parentheses around both the top and bottom to indicate that we had these expressions together before we ever thought about multiplying them by anything. We need those parentheses because both the top and bottom are broken up into two terms by the minus signs. The distributive property says we have to multiply both of the fractions inside the parentheses by 3(x + 2).

This is an excellent idea because it gets rid of all the denominators on both the top and bottom. We now have

a simple fraction. We will still want to simplify. On both the top and bottom there are parentheses we should remove.

Now we can factor and cancel.

and the answer is