Answer:
[tex]\frac{7x}{x^2 - 10x + 21} / \frac{x + 7}{7}[/tex]
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):
[tex]\frac{7x}{x^2 - 10x + 21} / \frac{x + 7}{7}[/tex]
This gives
[tex]\frac{7x}{x^2 - 10x + 21} * \frac{7}{x + 7}[/tex]
Set the denominator to 0
[tex](x^2 - 10x + 21)(x + 7) = 0[/tex]
Solve for x
[tex](x^2 - 7x - 3x + 21)(x + 7) = 0[/tex]
Factorize:
[tex](x(x - 7) - 3(x - 7))(x + 7) = 0[/tex]
[tex](x - 7)(x - 3)(x + 7) = 0[/tex]
This implies that:
[tex]x = 7\ or\ x = 3\ or\ x = -7[/tex]
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.
