To determine the value of [tex]\( x \)[/tex] for which the rational expression [tex]\(\frac{x-4}{4+x}\)[/tex] is undefined, we need to focus on the denominator of the expression. A rational expression becomes undefined when its denominator is equal to zero because division by zero is undefined in mathematics.
Given the expression:
[tex]\[ \frac{x-4}{4+x} \][/tex]
The denominator of this expression is:
[tex]\[ 4 + x \][/tex]
To find the value of [tex]\( x \)[/tex] that makes the expression undefined, we need to set the denominator equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ 4 + x = 0 \][/tex]
Subtract 4 from both sides:
[tex]\[ x = -4 \][/tex]
Therefore, the rational expression [tex]\(\frac{x-4}{4+x}\)[/tex] is undefined when [tex]\( x = -4 \)[/tex].
Comparing this solution to the provided answer choices, the correct answer is:
B. [tex]\(-4\)[/tex]
