Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Ask your questions and receive precise answers from experienced professionals across different disciplines. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

For what value of [tex]x[/tex] is the rational expression below undefined?

[tex]\[ \frac{3x - 12}{9 - x} \][/tex]

A. -4
B. 4
C. -9
D. 9


Sagot :

To determine for which value of [tex]\( x \)[/tex] the rational expression [tex]\(\frac{3x-12}{9-x}\)[/tex] is undefined, we need to focus on the denominator of the expression. A rational expression is undefined when its denominator is equal to zero.

Given the rational expression:
[tex]\[ \frac{3x-12}{9-x} \][/tex]

We need to find the value of [tex]\( x \)[/tex] that makes the denominator [tex]\( 9 - x \)[/tex] equal to zero.

Set the denominator equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ 9 - x = 0 \][/tex]

To isolate [tex]\( x \)[/tex], add [tex]\( x \)[/tex] to both sides of the equation:
[tex]\[ 9 = x \][/tex]

So, [tex]\( x = 9 \)[/tex].

Therefore, the rational expression [tex]\(\frac{3x-12}{9-x}\)[/tex] is undefined when [tex]\( x = 9 \)[/tex].

The correct answer is:
[tex]\[ \boxed{9} \][/tex]