# 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).