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Find the non-permissible replacement for [tex]n[/tex] in this expression:

[tex]\[ \frac{n-2}{n+8} \][/tex]

Enter the correct answer.


Sagot :

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]
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