To determine the value of [tex]\( x \)[/tex] for which the rational expression [tex]\(\frac{3x - 5}{x - 6}\)[/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. Therefore, we need to identify the value of [tex]\( x \)[/tex] that makes the denominator zero.
The denominator in the given expression is:
[tex]\[ x - 6 \][/tex]
To find the value of [tex]\( x \)[/tex] that makes this zero, we set the denominator equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ x - 6 = 0 \][/tex]
Adding 6 to both sides, we get:
[tex]\[ x = 6 \][/tex]
Thus, the rational expression [tex]\(\frac{3x - 5}{x - 6}\)[/tex] is undefined when [tex]\( x = 6 \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{6} \][/tex]
