What is the value of the rational expression below when [tex][tex]$x$[/tex][/tex] is equal to 3?

[tex]\[
\frac{12-x}{x-6}
\][/tex]

A. -3
B. 3
C. -9
D. 9



Answer :

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