To find the nonpermissible replacement for [tex]\( y \)[/tex] in the expression [tex]\(\frac{5}{9y}\)[/tex], we need to determine when the denominator of the fraction becomes zero. A fraction is undefined when its denominator is zero, so we set the denominator equal to zero and solve for [tex]\( y \)[/tex].
The expression in the denominator is [tex]\( 9y \)[/tex]. We set it equal to zero:
[tex]\[ 9y = 0 \][/tex]
Next, we solve for [tex]\( y \)[/tex]. To isolate [tex]\( y \)[/tex], we divide both sides of the equation by 9:
[tex]\[ y = \frac{0}{9} \][/tex]
Simplifying the right side, we get:
[tex]\[ y = 0 \][/tex]
So, the nonpermissible replacement for [tex]\( y \)[/tex] in the expression [tex]\(\frac{5}{9y}\)[/tex] is [tex]\( y = 0 \)[/tex].
Therefore, the nonpermissible value of [tex]\( y \)[/tex] is [tex]\( 0 \)[/tex].
