Excluded Values and Domain of Rational Functions

By: Andrea Bent and Camri Taylor

First Example...

Finding excluded value:   

First, you take the denominator and factor it out, so:

As you can see, you factor it out and you get the factors (x-3)(x-1).

Next, you must set each factor equal to zero and solve.

x-3=0                             x-1=0

x=3                                 x=1

3 and 1 are the excluded values.

The domain is all real  numbers except for 3 and 1.

Second example...

It is already fully factored so you take the denominator and set it equal to zero:

x-1=0

x=1  

The domain is all real numbers except for 1.

Example 3...

To find the excluded values, you must set the x in the denominator equal to zero.

x=0

This shows that the excluded value is zero. The domain is all real numbers except for zero.

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