To determine for which value of [tex]\( x \)[/tex] the given rational expression
[tex]\[
\frac{x-4}{x-6}
\][/tex]
is equal to zero, we need to focus on when the numerator of the fraction is equal to zero. This is because a rational expression equals zero when its numerator is zero (provided the denominator is not zero).
Given the rational expression:
[tex]\[
\frac{x-4}{x-6}
\][/tex]
Step-by-step solution:
1. Identify the numerator of the rational expression:
The numerator of the rational expression is [tex]\( x - 4 \)[/tex].
2. Set the numerator equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[
x - 4 = 0
\][/tex]
3. Solve this equation for [tex]\( x \)[/tex]:
[tex]\[
x = 4
\][/tex]
Therefore, the rational expression [tex]\(\frac{x-4}{x-6}\)[/tex] is equal to zero when [tex]\( x = 4 \)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{4}
\][/tex]
