To identify the nonpermissible replacement for [tex]\( b \)[/tex] in the expression [tex]\(\frac{b-7}{b-1}\)[/tex], we need to determine where the denominator equals zero. This is crucial because division by zero is undefined in mathematics.
Here are the steps to find the nonpermissible replacement:
1. Identify and set the denominator equal to zero:
[tex]\[
b - 1 = 0
\][/tex]
2. Solve the equation for [tex]\( b \)[/tex]:
[tex]\[
b = 1
\][/tex]
The value [tex]\( b = 1 \)[/tex] makes the denominator zero, which results in the expression being undefined.
Therefore, the nonpermissible replacement for [tex]\( b \)[/tex] in the expression [tex]\(\frac{b-7}{b-1}\)[/tex] is:
[tex]\[
\boxed{1}
\][/tex]
