To determine the nonpermissible replacement for [tex]\( n \)[/tex] in the expression
[tex]\[
\frac{n-8}{n-8},
\][/tex]
we need to find the values of [tex]\( n \)[/tex] that make the denominator equal to zero. Division by zero is undefined, hence these are the values for which the expression is undefined.
Here's the step-by-step process:
1. Identify the denominator of the expression:
[tex]\[
n - 8
\][/tex]
2. Set the denominator equal to zero to find the critical values:
[tex]\[
n - 8 = 0
\][/tex]
3. Solve for [tex]\( n \)[/tex]:
[tex]\[
n = 8
\][/tex]
So, the expression [tex]\(\frac{n-8}{n-8}\)[/tex] is undefined when [tex]\( n \)[/tex] is 8. Thus, the nonpermissible replacement for [tex]\( n \)[/tex] is:
[tex]\[
\boxed{8}
\][/tex]
