Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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

Sagot :

GinnyAnswer
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]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.