Adding and Subtracting Rational Expressions with Different Denominators
Example 1
Find:
Solution
Step 1 Find the LCD. 

Factor each denominator.


The LCD is w(w  6)
Â· 2
Â· 2
Â· y. 

Step 2 Rewrite each
rational expression
with the LCD as
the denominator. 

Step 3 Add (or subtract) the numerators.
The denominator stays the same. 

Subtract the numerators. 

Distribute the 7. 

Step 4 Reduce to lowest terms. 

The numerator cannot be factored using integers. Since there are no
factors, other than 1 or 1, common to the numerator and denominator,
the expression is in lowest terms.So,
Example 2
Find:
Solution
Step 1 Find the LCD. 

Factor each denominator.


The LCD is (x  3)(x
 3)(x + 3). 

Step 2 Rewrite each rational expression
with the LCD as the denominator. 

Step 3 Add (or subtract) the numerators. The denominator stays the
same. 

Subtract the numerators. 

In the numerator,
distribute the x and the 3. 

Combine like terms. 

Step 4 Reduce to lowest terms. 

The numerator cannot be factored over the integers.
Since there are no factors, other than 1 or 1, common to the numerator
and the denominator, the expression is in lowest terms.
So,
