To determine the nonpermissible value for [tex]\( a \)[/tex] in the expression [tex]\( \frac{a^2}{2a - 6} \)[/tex], we need to identify the value that makes the denominator zero. When the denominator is zero, the expression becomes undefined.
Given the denominator [tex]\( 2a - 6 \)[/tex], we set it equal to zero and solve for [tex]\( a \)[/tex]:
[tex]\[ 2a - 6 = 0 \][/tex]
Add 6 to both sides:
[tex]\[ 2a = 6 \][/tex]
Now, divide both sides by 2:
[tex]\[ a = 3 \][/tex]
So, the nonpermissible value for [tex]\( a \)[/tex] is:
[tex]\[ \boxed{3} \][/tex]
This is the value for [tex]\( a \)[/tex] that makes the denominator zero, rendering the expression undefined. Therefore, [tex]\( a = 3 \)[/tex] is the nonpermissible replacement for [tex]\( a \)[/tex] in the given expression.
