Example 1A: Adding Rational Expressions with Like Denominators
The rules for adding rational expressions are the same as the rules
for adding fractions. If the denominators are the same, you add the
numerators and keep the common denominator.
Add. Simplify your answer.
Combine like terms in the numerator. Divide out
common factors.
Simplify.
Example 1B: Adding Rational Expressions with Like Denominators
Example 1C: Adding Rational Expressions with Like Denominators
Add. Simplify your answer.
Add. Simplify your answer.
Combine like terms in the
numerator.
Combine like terms in the
numerator.
Factor. Divide out common
factors.
Factor. Divide out common
factors.
Simplify.
Simplify.
Check It Out! Example 1a
Add. Simplify your answer.
Combine like terms in the numerator. Divide out
common factors.
=2
Simplify.
Check It Out! Example 1b
Add. Simplify your answer.
Combine like terms in the
numerator.
Factor. Divide out common
factors.
Simplify.
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Example 2: Subtracting Rational Expressions with Like Denominators
Subtract. Simplify your answer.
To subtract rational expressions with like denominators,
remember to add the opposite of each term in the second
numerator.
Subtract numerators.
Combine like terms.
Factor. Divide out common
factors.
Simplify.
Check It Out! Example 2a
Subtract. Simplify your answer.
Caution
Make sure you add the opposite of all the terms in the numerator
of the second expression when subtracting rational expressions.
Subtract numerators.
Combine like terms.
Factor. Divide out common
factors.
Simplify.
Check It Out! Example 2b
Subtract. Simplify your answer.
Subtract numerators.
Combine like terms.
Factor. There are no
common factors.
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