Question

Find the domain of h(x)=x-3/x^3-36x

Answer 1

There is some ambiguity here which could be removed by using parentheses.  I'm going to assume that you actually meant:

               x-3

h(x) = ---------------

          (x^3-36x)

To determine the domain of this function, factor the denominator:

x^3 - 36x = x(x^2 - 36) = x(x-6)(x+6)

The given function h(x) is undefined when the denominator = 0, which happens at {-6, 0, 6}.

Thus, the domain is "the set of all real numbers not equal to -6, 0 or 6."

Symbolically, the domain is   (-infinity, -6) ∪ (-6, 0) ∪ (0, 6) ∪ (6, +infinity).