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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
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