The tutor explains the idea behind non-permissible values.

In high school math, non-permissible values become important. Yet, they root back to elementary school:

“You can’t divide by zero,” uttered in metallic timbre, is recalled by many from then.

A rational expression is defined to be

polynomial/polynomial

an example being

(2x-5)/(x²-x-12)

Fundamentally, such an expression is division, since by definition,

a/b = a÷b

Accepting that we can’t divide by zero, it follows that the bottom of the fraction mustn’t be zero. The bottom of the fraction is also called the denominator:

numerator/denominator

We arrive at the condition that the denominator mustn’t equal zero. Then, the values that would make it zero are the non-permissible values.

Example 1:

Give the non-permissible values of (2x+4)/(x²+3x)

Solution:

First, we factor the denominator:

(2x+4)/(x(x+3))

Now we observe that if x=0 or x=-3, the denominator will be zero. Therefore, 0 and -3 are the non-permissible values.

Example 2:

Give the non-permissible values of (x+5)/(x²-25)

Solution:

Once again, we factor the denominator:

(x+5)/((x+5)(x-5))

We see that the denominator will be zero if x=-5 or if x=5. Therefore, -5 and 5 are the non-permissible values.

Some people ask, Can’t you cancel the (x+5) top and bottom, to arrive at

1/(x-5) ?

Since that cancellation is actually division, you can only do so if x+5≠0. Therefore, potential cancellation does not change non-permissible values.

This is a first look at non-permissible values. I’ll probably do a follow-up.

HTH:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.