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

[tex]\frac{10-z}{7+x}[/tex]

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

Answer :

To determine which value of [tex]\( x \)[/tex] makes the rational expression [tex]\(\frac{10-z}{7+x}\)[/tex] undefined, we need to focus on the denominator. A rational expression is undefined if its denominator is equal to zero.

Step 1: Set the denominator equal to zero.

[tex]\[ 7 + x = 0 \][/tex]

Step 2: Solve for [tex]\( x \)[/tex].

- Subtract 7 from both sides of the equation to isolate [tex]\( x \)[/tex].

[tex]\[ x = -7 \][/tex]

The expression becomes undefined when [tex]\( x = -7 \)[/tex].

Therefore, the value of [tex]\( x \)[/tex] that makes the expression [tex]\(\frac{10-z}{7+x}\)[/tex] undefined is [tex]\( x = -7 \)[/tex].

So, the correct answer is option C: -7.

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