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Math

Attribution

Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in September 2020. This work is licensed under a Creative Commons BY 4.0 International License.

Adding and Subtracting Rational Expressions

 

CASE 1) Adding and Subtracting Rational Expressions with Common Variable Denominators: in this case, we only need to add/subtract the numerators.
Example: Subtract
We only need to subtract the numerators:

 

CASE 2) Adding and Subtracting Rational Expressions with Unlike Variable Denominators: in this case, we find a common denominator first and then proceed with the addition or subtraction.

 

Example: Add
To add these rational expressions, we need to find their common denominator. Since the denominators have nothing in common their common denominator is equal to their product:.
So, we multiply the first fraction by and multiply the second fraction by:

We then expand the numerators of each expression and add them together:

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