To determine the nonpermissible replacement for [tex]\( y \)[/tex] in the expression [tex]\(\frac{y^2}{3y - 9}\)[/tex], we need to identify the values of [tex]\( y \)[/tex] that make the denominator equal to zero. If the denominator is zero, the expression becomes undefined.
Given the expression:
[tex]\[
\frac{y^2}{3y - 9}
\][/tex]
First, consider the denominator:
[tex]\[
3y - 9
\][/tex]
We need to find the value of [tex]\( y \)[/tex] that satisfies:
[tex]\[
3y - 9 = 0
\][/tex]
Solve for [tex]\( y \)[/tex] by isolating [tex]\( y \)[/tex]:
[tex]\[
3y - 9 = 0
\][/tex]
Add 9 to both sides of the equation:
[tex]\[
3y = 9
\][/tex]
Now, divide both sides by 3:
[tex]\[
y = \frac{9}{3} = 3
\][/tex]
Thus, the value [tex]\( y = 3 \)[/tex] is the nonpermissible value because it makes the denominator zero, resulting in an undefined expression.
Hence, the nonpermissible replacement for [tex]\( y \)[/tex] in the given expression is:
[tex]\[
\boxed{3}
\][/tex]
