\[ f(x)=x-8 \quad g(x)=\frac{9}{x} \] Find $\frac{g}{f}$. Then, give its domain using an interval or union of intervals. Simplify your answers. \[ \left(\frac{g}{f}\right)(x)=[ \] Domain of $\frac{g}{f}$;

Step 1 ：To find \(\frac{g}{f}(x)\), we divide the function \(g(x)\) by \(f(x)\), which gives us \(\frac{g(x)}{f(x)} = \frac{\frac{9}{x}}{x-8}\).

Step 2 ：To simplify this, we multiply the numerator and the denominator by \(x\) to get rid of the fraction in the numerator, resulting in \(\frac{g}{f}(x) = \frac{9}{x(x-8)}\).

Step 3 ：To find the domain of \(\frac{g}{f}\), we set the denominator equal to zero and solve for \(x\), giving us the equation \(x(x-8) = 0\).

Step 4 ：Setting each factor equal to zero gives the solutions \(x = 0\) and \(x = 8\). These are the values that \(x\) cannot take, so the domain of \(\frac{g}{f}\) is all real numbers except \(0\) and \(8\).

Step 5 ：\(\boxed{\text{Domain of } \frac{g}{f}: (-\infty, 0) \cup (0, 8) \cup (8, \infty)}\)