gloryyy3
Answered

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For what value of [tex]x[/tex] is the rational expression below equal to zero?

[tex]\[
\frac{3x + 15}{6 - x}
\][/tex]

A. -6
B. 5
C. -5
D. 6

Sagot :

GinnyAnswer
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]
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