# Excluded Value

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

## Example 1: Excluded Value of (*x*^{2} + 5*x* - 1)/(3*x* - 2)

The excluded value of a fraction

is the *x* value

that makes the denominator 0.

You already know that

the denominator cannot be 0.

So, to exclude the [excluded value]

from the solution set,

you should know

how to find the excluded value.

To find the excluded value,

set (denominator) = 0.

The denominator of this fraction is [3*x* - 2].

So set 3*x* - 2 = 0.

Move -2 to the right side.

And divide both sides by 3.

Then *x* = 2/3.

This is the excluded value of (*x*^{2} + 5*x* - 1)/(3*x* - 2).

## Example 2: Excluded Value of (*x* - 4)/(*x* - 4)(*x* + 1)

You might want to cancel the common factor (*x* - 4).

But when finding the excluded value,

don't cancel the common factor

and just set (denominator) = 0.

Then (*x* - 4)(*x* + 1) = 0.

Solve (*x* - 4)(*x* + 1) = 0.

1) *x* - 4 = 0

So *x* = 4.

2) *x* + 1 = 0

So *x* = -1.

So *x* = -1, 4.

Solving a quadratic equation by factoring