Find the domain of $f(x)=\frac{x+6}{x^{2}-x-12}$. Enter the solution in interval notation.
help (intervals)

Step 1 ：The function given is \(f(x)=\frac{x+6}{x^{2}-x-12}\).

Step 2 ：The domain of a function is the set of all possible input values (x-values) that will output real numbers. In this case, the function is a rational function, and the only values that are not in the domain are those that make the denominator equal to zero, because division by zero is undefined.

Step 3 ：So, we need to find the values of x that make the denominator equal to zero. The denominator of the function is \(x^{2}-x-12\).

Step 4 ：The solutions to the equation \(x^{2}-x-12=0\) are \(x=-3\) and \(x=4\). These are the values that make the denominator of the function equal to zero, and therefore are not in the domain of the function.

Step 5 ：All other real numbers are in the domain of the function.

Step 6 ：\(\boxed{\text{Final Answer: The domain of the function } f(x)=\frac{x+6}{x^{2}-x-12} \text{ is } (-\infty, -3) \cup (-3, 4) \cup (4, \infty)}\)