To determine for what value of [tex]\( x \)[/tex] the rational expression [tex]\(\frac{3x + 15}{6 - x}\)[/tex] is equal to zero, we need to identify when the numerator of the fraction is zero.
Let's analyze the numerator of the rational expression, which is [tex]\( 3x + 15 \)[/tex].
1. Set the numerator equal to zero:
[tex]\[
3x + 15 = 0
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
- Subtract 15 from both sides of the equation:
[tex]\[
3x = -15
\][/tex]
- Divide both sides by 3:
[tex]\[
x = \frac{-15}{3}
\][/tex]
Simplifying the right-hand side:
[tex]\[
x = -5
\][/tex]
Thus, the rational expression [tex]\(\frac{3x + 15}{6 - x}\)[/tex] is equal to zero when [tex]\( x = -5 \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-5}
\][/tex]
