TUTORIALS:
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Adding Rational Expressions with the Same
Denominator
Adding rational expressions with the same denominator is like adding
fractions with the same denominator.
Procedure —
To Add Rational Expressions with the Same Denominator
Step 1 Add the numerators.
Write this sum as the numerator over the common
denominator.
Step 2 Reduce to lowest terms.
Note:
Here’s an example of adding fractions:
Add and write the answer in lowest terms:
![](./articles_imgs/17/adding62.gif)
The denominators are the same. Add the
numerators and write the sum over the
common denominator, 4.
![](./articles_imgs/17/adding63.gif)
To reduce, cancel the common factor, 2, in
the numerator and denominator.
![](./articles_imgs/17/adding64.gif)
Thus,
![](./articles_imgs/17/adding65.gif)
Example 1
Find:
![](./articles_imgs/17/adding66.gif)
Solution
The denominators are the same.
|
![](./articles_imgs/17/adding67.gif) |
Step 1 Add the numerators. Write this sum
as the numerator over the common
denominator. |
![](./articles_imgs/17/adding68.gif) |
Combine the like terms in the numerator.
|
![](./articles_imgs/17/adding69.gif) |
Step 2 Reduce to lowest terms.
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First, factor the numerator and denominator.
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![](./articles_imgs/17/adding70.gif) |
Next, cancel the common factor, 5. |
![](./articles_imgs/17/adding71.gif) |
Thus,
![](./articles_imgs/17/adding72.gif)
Example 2
Find:
![](./articles_imgs/17/adding73.gif)
Solution
The denominators are the same.
|
![](./articles_imgs/17/adding74.gif) |
Step 1 Add the numerators. Write this
sum as the numerator over
the common denominator. |
![](./articles_imgs/17/adding75.gif) |
Combine the like terms in the
numerator.
|
![](./articles_imgs/17/adding76.gif) |
Step 2 Reduce to lowest terms.
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|
First, factor the numerator and
denominator.
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![](./articles_imgs/17/adding77.gif) |
Next, cancel the common factor,
x + 1. |
![](./articles_imgs/17/adding78.gif) |
Thus,
![](./articles_imgs/17/adding79.gif)
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