Function Operations and Inverses Quotient of two functions: Basic

Suppose that the functions $g$ and $f$ are defined as follows.
\[
\begin{array}{l}
g(x)=x-4 \\
f(x)=(x+6)(x+3)
\end{array}
\]
(a) Find $\left(\frac{g}{f}\right)(5)$
(b) Find all values that are NOT in the domain of $\frac{g}{f}$. If there is more than one value, separate them with commas.
(a) $\left(\frac{g}{f}\right)(5)=\square$
(b) Value(s) that are NOT in the domain of $\frac{g}{f}: \square$
Explanation
Check

Step 1 ：Find the value of \(g(5)\) by substituting \(x = 5\) into \(g(x) = x - 4\), which gives \(g(5) = 5 - 4 = 1\)

Step 2 ：Find the value of \(f(5)\) by substituting \(x = 5\) into \(f(x) = (x + 6)(x + 3)\), which gives \(f(5) = (5 + 6)(5 + 3) = 11 * 8 = 88\)

Step 3 ：Calculate \(\left(\frac{g}{f}\right)(5)\) by dividing \(g(5)\) by \(f(5)\), which gives \(\left(\frac{g}{f}\right)(5) = \frac{g(5)}{f(5)} = \frac{1}{88}\)

Step 4 ：\(\boxed{\left(\frac{g}{f}\right)(5) = \frac{1}{88}}\)

Step 5 ：Find the values of \(x\) that are not in the domain of \(\frac{g}{f}\) by setting \(f(x) = 0\) and solving for \(x\), which gives \((x + 6)(x + 3) = 0\)

Step 6 ：Setting each factor equal to zero gives the solutions \(x = -6\) and \(x = -3\)

Step 7 ：\(\boxed{\text{Values that are NOT in the domain of } \frac{g}{f}: -6, -3}\)