What are the excluded values for this quotient?
x^3-4/x^3-9 divided by 3x^3+9x/x^3+6x+9
A. 0,3
B. -3, -2, 0, 2, 3
C. -3, 3
D. -3, 0, 3
The excluded values for this quotient are the values that make the denominator(s) equal to zero, since division by zero is undefined.
For the first fraction, the denominator is x^3 - 9. This expression factors as (x-3)(x^2+3x+9). So, x = 3 is an excluded value.
For the second fraction, the denominator is x^3 + 6x + 9, which can be factored as (x+3)(x^2-3x+3). So, x = -3 is an excluded value.
Therefore, the excluded values for the entire quotient are x = 3 and x = -3.
The correct answer is C. -3, 3.