Question
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
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
Answers
GPT 3.5
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.
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.