How to find the excluded value of a rational expression: examples and their solutions.
Example 1: Excluded Value of (x2 + 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)
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