Adding and Subtracting Rational Expressions with Identical Denominators
We can multiply or divide any rational expressions, but we add or subtract only
rational expressions with identical denominators. So when the denominators are not
the same, we must find equivalent forms of the expressions that have identical
denominators. In this section we will review the idea of the least common denominator
and will learn to use it for addition and subtraction of rational expressions.
It is easy to add or subtract fractions with identical denominators. For example,
In general, we have the following definition.
Addition and Subtraction of Rational Numbers
If b ≠ 0, then
Rational expressions with identical denominators are added or subtracted in the
same manner as fractions.
Example 1
Identical denominators
Perform the indicated operations.
Solution


Add the numerators. 


Reduce. 


Add the numerators. 


Combine like terms. 


Factor. 

= 2 
Reduce to its lowest terms. 
c) The polynomials in the numerators are treated as if they were in parentheses:
Helpful hint
You can remind yourself of the
difference between addition
and multiplication of fractions
with a simple example: If you
and your spouse each own
1/7 of Microsoft, then together
you own 2/7 of
Microsoft. If you own 1/7 of Microsoft, and give 1/7 of
your stock to your child, then
your child owns 1/49 of
Microsoft.
