Question

Select the correct answer. For which quotient is x=7 an excluded value?

Answer 1

A

Explanation:

Answer 2

`(7x)/(x^2 - 10x + 21) / (x + 7)/(7)`

Explanation:

Given

See attachment

To answer this question, we start by equating the denominators of each option to 0; then, solve for x

(a):

`(7x)/(x^2 - 10x + 21) / (x + 7)/(7)`

This gives

`(7x)/(x^2 - 10x + 21) * (7)/(x + 7)`

Set the denominator to 0

`(x^2 - 10x + 21)(x + 7) = 0`

Solve for x

`(x^2 - 7x - 3x + 21)(x + 7) = 0`

Factorize:

`(x(x - 7) - 3(x - 7))(x + 7) = 0`

`(x - 7)(x - 3)(x + 7) = 0`

This implies that:

`x = 7\ or\ x = 3\ or\ x = -7`

From above, one of the values of x is 7.

This implies that x = 7 is an excluded value for this quotient.

Other options do not need to be checked, since there is only one answer.