Learning Resources
Lesson
To add or subtract rational expressions with the same denominator, add (or subtract) the numerators, writing the result over the common denominator. Then express the answer in simplest terms. This is exactly the same procedure as adding rational numbers.
The examples below will illustrate this process.
Example 1
Subtract: 
Solution
Example 2
Add: 
Solution
Example 3
Subtract: 
Solution
If the denominators are additive inverses of each other (i.e. their sum is zero), the two denominators can be made equal by multiplying one of the fractions by 
. This is shown in the following example.
Example 4
Subtract: 
Solution
To add or subtract rational expressions with different denominators, we first change them to equivalent expressions with the same denominator, viz. the least common denominator (LCD). This procedure is shown in the following examples.
Example 1
Add: 
Solution
Example 2
Subtract: 
Solution
Example 3
Subtract: 
Solution
What values must be excluded from the replacement set for Example 3 above?
Example 4
Add: 
Solution
What values must be excluded from the replacement set of Example 4 above?
Activity
For each of the following, perform the indicated operations and express the answer in simplest terms.
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Test Yourself
For each of the following, perform the indicated operations and express the answer in simplest terms.
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