1. Adding and Subtracting Rational Expressions
Section 11.3
Adding and Subtracting Rational Expressions

2. Common Denominator
The key to adding and subtracting fractions is to get a common denominator.
For example, the operation
cannot be performed without converting it to

3. General Rules Step 1: Combine the numerators together.
Step 2: Put the sum or difference found in step 1 over the common denominator.
Step 3: Reduce to lowest terms.

4. Examples with a common denominator:

5. Examples:

6. Example:
We still need to cancel and reduce!

7. A common denominator is generally chosen to be the least common denominator (LCD) of the denominators.
For rational numbers and rational expressions, this can be thought of as the smallest number or expression that is divisible by every term.

8. Finding a common denominator
Cannot add because the denominators are different
What is your common denominator? (x+2)(x+5)
So the first fraction is missing: (x+5)
The second fraction is missing: (x+2)

9. If you want to add something to a fraction you must add it on both the top and the bottom of the fraction.

10. Combine like terms and simplify… don’t forget restrictions!
Restrictions are:
The problem cannot be simplified.

11. Example:

12. Don’t forget to cancel!
Restrictions are: