Objectives 

• Reducing to Lowest Terms

• Finding the Least Common Denominator

• Mixed Quotients

Examples

• Example 1

• Example 2

• Example 3

• Example 4

Simply stated, a common denominator is any expression which 
can be evenly divided by each of the original denominators.

For example, the fractions 1/4, 1/5, 1/10 will have common denominators 20,40,60, etc.

We will be most interested in constructing the "Least Common 
Denominator (LCD)," that is, the smallest expression which can 
"absorb" each individual denominator.

The LCD of 1/4, 1/5 , 1/10 is 20.

By using the LCD, we will be able to simplify our final answer more quickly.

To combine rational expressions which contain variables, we also need to construct the LCD.

Note: You will have more success in constructing the LCD for a collection of rational expressions if you factor each denominator separately before you attempt the problem.

For example, given the addition problem:  ,
 

we first factor each denominator and get 

.
 

Now we can see that the LCD will be  .

Note: An alternate common denominator would be 

, 

but this is "bigger" than we need.

Using the LCD ,  , we "adjust" each numerator of the original addition problem so that we can combine the fractions:

After multiplying out and combining like terms, this numerator simplifies to  .

So our final answer in factored form, reduced to lowest terms is: