What are the excluded values?

[tex]\[ \frac{x-7}{x+9} \][/tex]

A. [tex]\( x = 7 \)[/tex]
B. [tex]\( x = 9 \)[/tex]
C. [tex]\( x = -9 \)[/tex]
D. None of the above



Answer :

We start with the given rational function:

[tex]\[ \frac{x-7}{x+9} \][/tex]

For any rational expression, the values of [tex]\( x \)[/tex] that make the denominator zero are considered excluded values because division by zero is undefined.

Here, the denominator of the rational function is [tex]\( x + 9 \)[/tex]. We set the denominator equal to zero to find the excluded values:

[tex]\[ x + 9 = 0 \][/tex]

Solving this equation for [tex]\( x \)[/tex]:

[tex]\[ x = -9 \][/tex]

Thus, the value [tex]\( x = -9 \)[/tex] makes the denominator zero, and hence it is the excluded value.

From the list provided:
- [tex]\( x = 7 \)[/tex]: This does not make the denominator zero, so it is not an excluded value.
- [tex]\( x = 9 \)[/tex]: This does not make the denominator zero, so it is not an excluded value.
- [tex]\( x = -9 \)[/tex]: This makes the denominator zero, so it is an excluded value.
- None of the above: Since [tex]\( x = -9 \)[/tex] is indeed an excluded value, this option is incorrect.

Therefore, the correct answer is:

[tex]\[ x = -9 \][/tex]