When looking at a rational function, Jamal and Angie have two different thoughts. Jamal says that the function is defined at x = -3, x = -4, and x = 6. Angie says that the function is undefined at those x values. Describe a situation where Jamal is correct, and describe a situation where Angie is correct. Is it possible for a situation to exist that they are both correct? Justify your reasoning.

Question

myininaya · Answer

Hint for part of this: Think of a fraction. A fraction doesn't exist when its bottom is zero. 
like x+3 is zero when x=-3.
The fraction 1/(x+3) does not exist at x=-3.

anonymous · Answer

Angie is correct if this were the case$$\frac{ 1 }{ (x+3)(x+4)(x-6) }$$ because if any of those values were put it in, the denominator would be zero. Can't divide by zero...now can we?

Jamal would be correct if $$(x+3) +(x-4) + (x-6)$$
Both could be correct if this were the case:
$$\frac{ (x+3)(x+4)(x-6) }{ (x+3)(x+4)(x-6) }$$ because even though the bottom is zero, so is the top. 0/0 is still zero. So..maybe we can divide by zero after all.