Excluded Value

Excluded Value

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

Example 1: Excluded Value of (x2 + 5x - 1)/(3x - 2)

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

So set 3x - 2 = 0.

Move -2 to the right side.
And divide both sides by 3.

Then x = 2/3.

This is the excluded value of (x2 + 5x - 1)/(3x - 2).

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

Find the excluded value of the given expression. (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