To determine the nonpermissible value for [tex]\( n \)[/tex] in the expression [tex]\(\frac{n-2}{n+8}\)[/tex], we need to identify when the denominator equals zero. In any rational expression, the denominator must not be zero, because division by zero is undefined.
Given the expression:
[tex]\[
\frac{n-2}{n+8}
\][/tex]
We focus on the denominator [tex]\( n + 8 \)[/tex]. For the fraction to be defined, the denominator cannot be zero. Therefore, we solve the equation:
[tex]\[
n + 8 \neq 0
\][/tex]
To find the value of [tex]\( n \)[/tex] that would make the denominator zero, we solve for [tex]\( n \)[/tex]:
[tex]\[
n + 8 = 0
\][/tex]
Subtract 8 from both sides of the equation:
[tex]\[
n = -8
\][/tex]
Hence, [tex]\( n \)[/tex] cannot be [tex]\(-8\)[/tex] because it would make the denominator zero, which is undefined in mathematics. Therefore, the nonpermissible value for [tex]\( n \)[/tex] in the expression [tex]\(\frac{n-2}{n+8}\)[/tex] is:
[tex]\[
n = -8
\][/tex]
