# 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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