If X = (9b - 3ab) / (3/a - a/3), what is x?

[Aryan.8]

If x = (9b - 3ab)/(3/a - a/3), what is x?

(1) 9ab/(3+a) = 18/5
(2) b = 1


This question is present in Manhattan guide 2 in chapter Strategy:Combos.
It's official answer is A. However I have doubt in that.
In the official Manhattan guide explanation the equation is reformed into 3a(3b)(3-a)/(3-a)(3+a)) and then (3-a) is cancelled from top and the bottom.

However according to rules we can only cut some variables from numerator and denominator only when we are sure that they are not equal to zero. But here it is possible that (3-a) can be equal to 0. When I take a=3 and b=4/5 the equation 9ab/(3+a) = 18/5 is satisfied but now (3-a) cannot be cancelled from numerator and denominator.

If the second option b=1 is taken into consideration than it can be proved that a is never equal to 3 by substituting in the statement (1) equation.
So shouldn't the answer be "C" because both the statements are required to give an unambiguous answer?

For answer to be "A" shouldn't it be specified in the question that a is not equal to 3?

[esledge]

If x = (9b - 3ab)/(3/a - a/3), what is x?

.... But here it is possible that (3-a) can be equal to 0. ...

For answer to be "A" shouldn't it be specified in the question that a is not equal to 3?

Coincidentally, the concept of zero denominators was the subject of some recent discussion among Manhattan Prep instructors. There's published evidence that the GMAT does not always specify explicitly that a denominator is not equal to zero, because the restriction to real numbers on the GMAT means that non-zero denominators are implied. We aren't entirely sure when/why the writers will sometimes tell you explicitly anyway. [My guesses: Some individuals tend to explain more than others, so this might just be due to different question writers. Some problems might measure "too difficult" without the given constraint. A given constraint (that something isn't zero) might be a hint that you need to divide by that thing (i.e. the writers are giving you "permission," and thus the suggestion, to divide).]

On this question, the answer to "what is x?" could be "I don't know" or "I don't know which of these values it is" or "It depends on [some unknown variable that can't be cancelled]," which would indicate an Insufficient statement or statements. But the numerical answer(s) would have to be real numbers. It is understood that the answer to "what is x?" can't be undefined (which no one knows the value of, because it's not a real number). Thus, I would argue that the question stem equation itself rules out both a=3 and a = 0, both of which would make an undefined fraction somewhere if you plug them in.

So with that in mind, if you cancel (a - 3) from top and bottom when rephrasing, you are eliminating a solution that wasn't valid anyway.

(Similarly, Stmt (1) implies that 3+a =/=0, or a is not equal to -3, either.)