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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.

Rational Expressions and Non-Permissible Values:


rational expression is the ratio of two polynomials: 


Non-Permissible Values: 

Non-permissible values are values of the variable(s) that make the denominator of a rational expression equal to zero. In order to find the non-permissible values of a rational expression one has to set the denominator equal to zero and solve it for the variable. Below, we look at few examples on how to find non-permissible values. 


Example: Find non-permissible values of .
We set the denominator equal to zero:


Now, we solve for x:

Therefore,  are the non-permissible values. 
WARNING!! Do not use the simplified form of a rational expression to find its non-permissible values. When we simplify a rational expression, we might lose some of its non-permissible values.


Example: Find non-permissible values of.
To find the non-permissible values we have to set the denominator equal to zero:

Since we have the product of two terms here, we have to set each term equal to zero and solve for x:

Therefore, the non-permissible values are 
Attention! If we simplify the expression, we get

which has no non-permissible values. Therefore, we have to find non-permissible values before we simplify an expression.



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