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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:
The denominators are the same. Add the
numerators and write the sum over the
common denominator, 4.
To reduce, cancel the common factor, 2, in
the numerator and denominator.
Thus,
Example 1
Find:
Solution
| The denominators are the same.
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| Step 1 Add the numerators. Write this sum
as the numerator over the common
denominator. |
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| Combine the like terms in the numerator.
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| Step 2 Reduce to lowest terms.
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| First, factor the numerator and denominator.
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| Next, cancel the common factor, 5. |
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Thus,
Example 2
Find:
Solution
| The denominators are the same.
|
 |
| Step 1 Add the numerators. Write this
sum as the numerator over
the common denominator. |
 |
| Combine the like terms in the
numerator.
|
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| Step 2 Reduce to lowest terms.
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| First, factor the numerator and
denominator.
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| Next, cancel the common factor,
x + 1. |
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Thus,
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