Adding and Subtracting Rational Expressions

1. Adding and subtracting rational expressions is similar to adding and
subtracting fractions .

2. Adding Rational Expressions: To add rational expressions with the
same denominator , add the numerators and put the sum over the
common denominator . Thus, if and are two rational
expressions:

Be sure to write your final answer in lowest terms . (Factor and
cancel common factors .)

3. Subtract Rational Expressions: To subtract rational expressions
with the same denominator , subtract the numerators and put the
difference over the common denominator. Thus, if are
two rational expressions:

Be sure to write your final answer in lowest terms .

4. Hint: Be sure to subtract the entire numerator of the rational
expression after the minus sign.

It is a good idea to use parentheses when subtracting . Thus,
and distribute the minus sign through R.

5. Add Rational Expressions with Different Denominators : (See
page 418.)

Step 1: Find the least common denominator (LCD) of all
denominators.

Step 2: Rewrite each rational expression as an equivalent rational
express with this LCD as the denominator .

Step 3: Add the new numerators and place this sum over the LCD.

Step 4: Write in lowest terms. (Factor and cancel common factors.)

6. Subtract Rational Expressions with Different Denominators:
(This is similar to adding except you subtract the numerators.)

Step 1: Find the least common denominator (LCD) of all
denominators.

Step 2: Rewrite each rational expression as an equivalent rational
express with this LCD as the denominator.

Step 3: Subtract the new numerators and place this difference over
the LCD. (Place parentheses around the numerator after the minus
sign and distribute the minus.)

Step 4: Write in lowest terms. (Factor and cancel common factors