High School

Which of the following values of [tex]x[/tex] makes the rational expression below undefined?

[tex]\frac{16x}{7-x}[/tex]

A. 7
B. -7
C. 16
D. -16

Answer :

To determine when the rational expression [tex]\(\frac{16x}{7-x}\)[/tex] is undefined, we need to focus on the denominator, [tex]\(7-x\)[/tex]. A rational expression becomes undefined when its denominator is equal to zero because division by zero is not allowed in mathematics.

1. Start with the denominator: [tex]\(7 - x\)[/tex]

2. Set the denominator equal to zero to find the value of [tex]\(x\)[/tex] that makes it zero:
[tex]\[
7 - x = 0
\][/tex]

3. Solve for [tex]\(x\)[/tex]:
[tex]\[
-x = -7
\][/tex]

Multiply both sides by [tex]\(-1\)[/tex]:
[tex]\[
x = 7
\][/tex]

Therefore, the rational expression [tex]\(\frac{16x}{7-x}\)[/tex] is undefined when [tex]\(x = 7\)[/tex].

So, the correct choice is:

A. 7