To determine the value of the rational expression [tex]\(\frac{x-2}{x-5}\)[/tex] when [tex]\(x = 6\)[/tex], we need to substitute [tex]\(x\)[/tex] with 6 in the expression.
Let's go through the steps:
1. Substitute [tex]\(x = 6\)[/tex] into the expression:
[tex]\[
\frac{6-2}{6-5}
\][/tex]
2. Simplify the numerator:
[tex]\[
6 - 2 = 4
\][/tex]
3. Simplify the denominator:
[tex]\[
6 - 5 = 1
\][/tex]
4. Now we have:
[tex]\[
\frac{4}{1}
\][/tex]
5. Simplify the fraction:
[tex]\[
\frac{4}{1} = 4
\][/tex]
Therefore, the value of the rational expression when [tex]\(x = 6\)[/tex] is 4.
So, the correct answer is:
D. 4
