The domain of a function is all the possible input values (often variable x for simple equations) that will output real numbers.
For the function f(x)=(3x²-6x)/(x²-4), there is a denominator of (x²-4).
Any value of x that makes this denominator equals to 0 should not be included in the domain because division by 0 is undefined in real number arithmetic.
So first of all, we need to find the values of x that would make the denominator equal to 0, i.e., solve the equation x²-4=0.
Adding 4 to both sides of the equation gives us x² = 4.
The solutions to this equation are x = sqrt(4) and x = -sqrt(4), which are x = 2 and x = -2, respectively.
So, the values of x that are excluded from the domain are x = 2 and x = -2.
As the function does not contain anything else that would further restrict the domain, all other real numbers are included.
Therefore, the valid inputs for x, that is, the domain of the function, are all real numbers except for -2 and 2.
So, we can say that the domain of the function f(x)=(3x²-6x)/(x²-4) is all real numbers except -2 and 2.