To determine the value of the rational expression [tex]\(\frac{12 - x}{x - 6}\)[/tex] when [tex]\(x = 3\)[/tex], follow these steps:
1. Substitute [tex]\(x = 3\)[/tex] into the numerator:
The numerator of the expression is [tex]\(12 - x\)[/tex].
[tex]\[
12 - 3 = 9
\][/tex]
2. Substitute [tex]\(x = 3\)[/tex] into the denominator:
The denominator of the expression is [tex]\(x - 6\)[/tex].
[tex]\[
3 - 6 = -3
\][/tex]
3. Evaluate the rational expression:
Substitute the calculated numerator and denominator back into the rational expression:
[tex]\[
\frac{9}{-3}
\][/tex]
Simplify the fraction:
[tex]\[
\frac{9}{-3} = -3
\][/tex]
After completing these steps, the value of the rational expression [tex]\(\frac{12 - x}{x - 6}\)[/tex] when [tex]\(x = 3\)[/tex] is [tex]\(-3\)[/tex].
Hence, the correct answer is:
A. -3
