Question

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

Answer 1

Answer:

$\frac{7x}{x^2 - 10x + 21} / \frac{x + 7}{7}$

Step-by-step explanation:

Given

See attachment

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

(a):

$\frac{7x}{x^2 - 10x + 21} / \frac{x + 7}{7}$

This gives

$\frac{7x}{x^2 - 10x + 21} * \frac{7}{x + 7}$

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.