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

[tex]\frac{y^2}{3y-9}[/tex]

Enter the correct answer.


Sagot :

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]