Functions Quotient of two functions: Advanced Kailee -uppose that the functions $f$ and $g$ are defined as follows. Español \[ f(x)=\frac{x}{x-9} \quad g(x)=\frac{x+3}{x-9} \] Find $\frac{f}{g}$. Then, give its domain using an interval or union of intervals. Simplify your answers. \[ \begin{array}{l} \left(\frac{f}{g}\right)(x)=\square \\ \text { Domain of } \frac{f}{g}: \square \end{array} \] Explanation Check

Step 1 ：\(\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{\frac{x}{x-9}}{\frac{x+3}{x-9}}\)

Step 2 ：Multiply the numerator and the denominator by (x-9) to get rid of the denominator in both fractions: \(\left(\frac{f}{g}\right)(x) = \frac{x}{x+3}\)

Step 3 ：Set the denominator equal to zero and solve for x to find the domain: x + 3 = 0, x = -3

Step 4 ：The domain of the function is all real numbers except -3. In interval notation, this is: \(\boxed{(-\infty, -3) \cup (-3, \infty)}\)