Adding and Subtracting Rational Expressions with Different Denominators
We add or subtract rational expressions in the same way that we add or
subtract fractions.
You have already learned how to add and subtract rational expressions
with the same denominator. Now we will add and subtract rational
expressions with different denominators.
Procedure â€”
To Add (or Subtract) Rational
Expressions That Have Different Denominators
Step 1 Find the LCD.
Step 2 Rewrite each rational expression with the LCD as the
denominator.
Step 3 Add (or subtract) the numerators.
The denominator stays the same.
Step 4 Reduce to lowest terms.
We usually leave the answer in factored form.
Note:
To add (or subtract) fractions with
different denominators, say
follow these steps:
Step 1 Find the LCD.
24 = 2 Â· 2 Â· 2
Â· 3
15 = 3 Â· 5
LCD = 2 Â· 2
Â· 2 Â· 3
Â· 5 = 120
Step 2 Rewrite each fraction with the LCD
as the denominator.
Step 3 Add (or subtract) the numerators.
The denominator stays the same.
Step 4 Reduce to lowest terms.
Example 1
Find:
Solution
Thus,
Note:
In
, we CANNOT cancel w or x
because the operation in the numerator is
addition, not multiplication.
