Adding and Subtracting Rational Expressions with Different Denominators
Example 1
Find:
![](./articles_imgs/75/adding1.gif)
Solution
Step 1 Find the LCD. |
|
Factor each denominator.
|
![](./articles_imgs/75/adding2.gif) |
The LCD is w(w - 6)
· 2
· 2
· y. |
|
Step 2 Rewrite each
rational expression
with the LCD as
the denominator. |
![](./articles_imgs/75/adding3.gif) |
Step 3 Add (or subtract) the numerators.
The denominator stays the same. |
|
Subtract the numerators. |
![](./articles_imgs/75/adding4.gif) |
Distribute the -7. |
![](./articles_imgs/75/adding5.gif) |
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,
![](./articles_imgs/75/adding6.gif)
Example 2
Find:
![](./articles_imgs/75/adding7.gif)
Solution
Step 1 Find the LCD. |
|
Factor each denominator.
|
![](./articles_imgs/75/adding8.gif) |
The LCD is (x - 3)(x
- 3)(x + 3). |
|
Step 2 Rewrite each rational expression
with the LCD as the denominator. |
![](./articles_imgs/75/adding9.gif) |
Step 3 Add (or subtract) the numerators. The denominator stays the
same. |
|
Subtract the numerators. |
![](./articles_imgs/75/adding10.gif) |
In the numerator,
distribute the x and the -3. |
![](./articles_imgs/75/adding11.gif) |
Combine like terms. |
![](./articles_imgs/75/adding12.gif) |
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,
![](./articles_imgs/75/adding13.gif)
|