Adding and Subtracting Rational Expressions with Different Denominators
Example 1
Find:
Solution
| Step 1 Find the LCD. |
|
| Factor each denominator.
|
 |
| The LCD is w(w - 6)
· 2
· 2
· y. |
|
| Step 2 Rewrite each
rational expression
with the LCD as
the denominator. |
 |
| Step 3 Add (or subtract) the numerators.
The denominator stays the same. |
|
| Subtract the numerators. |
 |
| Distribute the -7. |
 |
| Step 4 Reduce to lowest terms. |
|
The numerator cannot be factored using integers. Since there are no
factors, other than 1 or
-1, common to the numerator and denominator,
the expression is in lowest terms.
So,
Example 2
Find:
Solution
| Step 1 Find the LCD. |
|
| Factor each denominator.
|
 |
| The LCD is (x - 3)(x
- 3)(x + 3). |
|
| Step 2 Rewrite each rational expression
with the LCD as the denominator. |
 |
| Step 3 Add (or subtract) the numerators. The denominator stays the
same. |
|
| Subtract the numerators. |
 |
| In the numerator,
distribute the x and the -3. |
 |
| Combine like terms. |
 |
| Step 4 Reduce to lowest terms. |
|
The numerator cannot be factored over the integers.
Since there are no factors, other than 1 or -1, common to the numerator
and the denominator, the expression is in lowest terms.
So,
