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

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

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

Answer :

To determine which value of [tex]\( x \)[/tex] makes the rational expression [tex]\(\frac{16-x}{7+x}\)[/tex] undefined, we need to find out when the denominator equals zero. A rational expression is undefined whenever its denominator is zero because division by zero is not allowed in mathematics.

Let's break it down step-by-step:

1. Identify the Denominator:
For the expression [tex]\(\frac{16-x}{7+x}\)[/tex], the denominator is [tex]\(7 + x\)[/tex].

2. Set the Denominator to Zero:
We want to find the value of [tex]\( x \)[/tex] that makes [tex]\(7 + x = 0\)[/tex].

3. Solve the Equation:
[tex]\[
7 + x = 0
\][/tex]

Subtract 7 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = -7
\][/tex]

4. Conclusion:
The value [tex]\( x = -7 \)[/tex] makes the denominator zero, and therefore, makes the expression undefined.

Therefore, the correct answer is A. -7.

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