Math 45

Sample 1st Midterm

Problem 1

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.

To multiply the top by   3x(x + 2),   put parentheses around the top and put a   3x(x + 2)   in front of the parentheses, and the same on the bottom. The parentheses then indicate that we had these expressions together before we ever thought about multiplying them by anything, but the parentheses say 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

Method 2 isquicker and easier, but Method 1 gives us a chance to review all four operations, addition, subtraction, multiplication, and division, of fractions.