Adding or Subtracting Rational Expressions with Different Denominators
Here is the procedure for adding (or subtracting) fractions.
Procedure
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.
Example
Add:
Step 4 Reduce.
The numerator cannot be factored. This rational expression is in lowest
terms.
We will leave the denominator in factored form.
So, the result is
. 
Note:
To factor 5x^{2 } 3x  2:
â€¢ Find two integers whose product is
5(2) = 10, and whose sum is 3.
They are 2 and 5.
â€¢ Use these integers to rewrite
5x^{2}  3x  2
as
5x^{2} + 2x  5x  2.
â€¢ Factor by grouping.
x(5x + 2)  1(5x + 2)
= (5x + 2)(x + 1)
To factor x^{2} + 5x  6:
â€¢ Find two integers whose product is 6 and whose sum is 5.
They are 1 and 6.
â€¢ Use these integers to write the
factorization (x  1)(x + 6).
