TUTORIALS:
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Subtracting Rational Expressions with the Same
Denominator
Subtracting rational expressions with the same denominator is like
subtracting fractions with the same denominator.
Procedure —
To Subtract Rational Expressions with the Same Denominator
Step 1 Subtract the numerators.
Write the difference as the numerator over the common
denominator.
Step 2 Reduce to lowest terms.
Note:
Here’s an example of subtracting
fractions:
Subtract and write the answer in lowest
terms:
The denominators are the same.
Subtract the numerators and write the
difference over the common denominator,
6.
![](./articles_imgs/1297/subtra81.gif)
To reduce, cancel the common factor, 2, in
the numerator and denominator.
![](./articles_imgs/1297/subtra82.gif)
Thus,
![](./articles_imgs/1297/subtra83.gif)
Example 1
Find:
![](./articles_imgs/1297/subtra84.gif)
Solution
The denominators are the same.
|
![](./articles_imgs/1297/subtra85.gif) |
Step 1 Subtract the numerators. Write the
difference as the numerator over the
common denominator. |
![](./articles_imgs/1297/subtra86.gif) |
Combine the like terms in the numerator. |
![](./articles_imgs/1297/subtra87.gif) |
Step 2 Reduce to lowest terms.
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First, factor the numerator and denominator. |
![](./articles_imgs/1297/subtra88.gif) |
There are no common factors to cancel. |
![](./articles_imgs/1297/subtra89.gif) |
Thus,
![](./articles_imgs/1297/subtra90.gif)
Example 2
Find:
![](./articles_imgs/1297/subtra91.gif)
Solution
The denominators are the same.
|
![](./articles_imgs/1297/subtra92.gif) |
Step 1 Subtract the numerators. Write
the difference as the numerator
over the common denominator. |
![](./articles_imgs/1297/subtra93.gif) |
Combine the like terms in the
numerator.
|
![](./articles_imgs/1297/subtra94.gif) |
Step 2 Reduce to lowest terms.
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First, factor the numerator and
denominator.
|
![](./articles_imgs/1297/subtra95.gif) |
Next, cancel the common factor,
x + 1. |
![](./articles_imgs/1297/subtra96.gif) |
Thus,
![](./articles_imgs/1297/subtra97.gif)
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