To determine the value of the rational expression [tex]\(\frac{6-x}{x+5}\)[/tex] when [tex]\(x = 2\)[/tex], we will follow these steps:
1. Substitute [tex]\(x = 2\)[/tex] into the expression:
[tex]\[
\frac{6-2}{2+5}
\][/tex]
2. Simplify the numerator:
[tex]\[
6 - 2 = 4
\][/tex]
3. Simplify the denominator:
[tex]\[
2 + 5 = 7
\][/tex]
4. Write the simplified form of the rational expression:
[tex]\[
\frac{4}{7}
\][/tex]
Therefore, when [tex]\(x = 2\)[/tex], the value of the rational expression [tex]\(\frac{6-x}{x+5}\)[/tex] is [tex]\(\frac{4}{7}\)[/tex].
Thus, the correct option is [tex]\(\frac{4}{7}\)[/tex].
