Adding and Subtracting Rational Expressions:

Note that rational expressions are simply algebraic fractions. Hence when performing addition or subtraction, they must follow ordinary rules for fractions.

Specifically they must have a common denominator [LCD]. Some examples will illustrate the point.

Example 1:

Text Box: Adding and Subtracting Rational Expressions with LIKE DENOMINATORS:
· Keep the common denominator
· Add or subtract the numerators
· State any restrictions – remember the denominators cannot equal 0.

Example 2:

Solution:

Text Box: Adding and Subtracting Rational Expressions with UNLIKE DENOMINATORS:
· Factor each denominator
· LCD ---àTake the highest exponent of each factor for algebraic factors
· LCD ---àFor numerical factors, take the LCD of the numbers
· Add or subtract the numerators, simplifying fully
· State any restrictions – remember the denominators cannot equal 0.

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