Excluded Value (Extraneous Solution)

Excluded Value (Extraneous Solution)

How to find the excluded value (extraneous solution) of a rational expression: examples and their solutions.

Example 1

Find the excluded value of the given fraction. (x^2 + 5x + 1)/(3x - 2)

The excluded value (extraneous solution) of a fraction
is the x value that makes the denominator 0.

To find the excluded value,
set '(denominator) = 0'.
3x - 2 = 0

Then x = 2/3.
This means x cannot be 2/3.

Example 2

Find the excluded value of the given fraction. (x + 4)/(x + 4)(x - 6)

Before cancelling x + 4,
first find the excluded value.

Set '(denominator) = 0'.
(x + 4)(x - 6) = 0

Then x = -4, 6.
This means x cannot be -4 and 6.