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

[tex]\[
\frac{2x + 4}{x - 7}
\][/tex]

A. -2
B. 2
C. 7
D. -7


Sagot :

To determine where the rational expression [tex]\(\frac{2x + 4}{x - 7}\)[/tex] is undefined, we need to look at the denominator. A rational expression is undefined wherever the denominator is equal to zero because division by zero is not defined in mathematics.

The denominator of the given expression is [tex]\(x - 7\)[/tex]. We need to find the value of [tex]\(x\)[/tex] that makes this denominator equal to zero.

Let's set the denominator equal to zero and solve for [tex]\(x\)[/tex]:
[tex]\[ x - 7 = 0 \][/tex]

Add 7 to both sides of the equation to isolate [tex]\(x\)[/tex]:
[tex]\[ x = 7 \][/tex]

Therefore, the rational expression [tex]\(\frac{2x + 4}{x - 7}\)[/tex] is undefined when [tex]\(x\)[/tex] is equal to 7.

Thus, the value of [tex]\(x\)[/tex] that makes the expression undefined is:

[tex]\[ \boxed{7} \][/tex]