How can I find the largest possible subset A of $\mathbb{R}$?

Question

So I have this equation $$f(x)= \frac{x^2}{(x-2)(x+3)}$$ and I need to find the largest possible subset $A$ of $\mathbb{R}$ that could form the domain of a function. Can anybody help me? I really don't know how to do this.

Answer 1

The question is: for what real numbers $x$ can you compute $f(x)$?

Well, what could possibly go wrong? Go through the steps you need to do to compute the function value:

Computing the square $x^2$ in the numerator can be done for all real numbers; the same holds for computing the product $(x-2)(x+3)$ in the denominator. But then you need to divide them. And although division by any real number other than zero is fine, division by zero is not allowed.

So you need to exclude the real numbers where $(x-2)(x+3)$ equals zero: $A$ consists of all real numbers other than $2$ and $-3$.