To determine for which value of [tex]\( x \)[/tex] the rational expression [tex]\(\frac{3x-12}{9-x}\)[/tex] is undefined, we need to focus on the denominator of the expression. A rational expression is undefined when its denominator is equal to zero.
Given the rational expression:
[tex]\[
\frac{3x-12}{9-x}
\][/tex]
We need to find the value of [tex]\( x \)[/tex] that makes the denominator [tex]\( 9 - x \)[/tex] equal to zero.
Set the denominator equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[
9 - x = 0
\][/tex]
To isolate [tex]\( x \)[/tex], add [tex]\( x \)[/tex] to both sides of the equation:
[tex]\[
9 = x
\][/tex]
So, [tex]\( x = 9 \)[/tex].
Therefore, the rational expression [tex]\(\frac{3x-12}{9-x}\)[/tex] is undefined when [tex]\( x = 9 \)[/tex].
The correct answer is:
[tex]\[
\boxed{9}
\][/tex]
