To find the nonpermissible replacement for [tex]\( b \)[/tex] in the given expression [tex]\( \frac{b-1}{b-7} \)[/tex], we need to identify the value of [tex]\( b \)[/tex] that makes the denominator zero. This is essential because division by zero is undefined in mathematics.
Let's analyze the denominator of the fraction:
[tex]\[ b - 7 \][/tex]
We set the denominator equal to zero and solve for [tex]\( b \)[/tex]:
[tex]\[ b - 7 = 0 \][/tex]
Adding 7 to both sides of the equation gives:
[tex]\[ b = 7 \][/tex]
Thus, the nonpermissible replacement for [tex]\( b \)[/tex] in the expression [tex]\( \frac{b-1}{b-7} \)[/tex] is [tex]\( 7 \)[/tex]. This means that if [tex]\( b \)[/tex] were 7, the denominator would be zero, which is not allowed. Therefore, the correct answer is:
[tex]\[ 7 \][/tex]
