Find the difference quotient of $f$; that is, find $\frac{f(x+h)-f(x)}{h}, h \neq 0$, for the following function. Be sure to simplify.
\[
f(x)=x^{2}-9 x+7
\]
$\frac{f(x+h)-f(x)}{h}=2 x+h-9 \quad($ Simplify your answer.)

Step 1 ：Given the function \(f(x)=x^{2}-9 x+7\)

Step 2 ：We are asked to find the difference quotient of \(f\), which is \(\frac{f(x+h)-f(x)}{h}, h \neq 0\)

Step 3 ：Substitute \(x+h\) into the function \(f(x)\) to get \(f(x+h) = (x+h)^{2}-9 (x+h)+7\)

Step 4 ：Subtract \(f(x)\) from \(f(x+h)\) to get \(f(x+h)-f(x) = (x+h)^{2}-9 (x+h)+7 - (x^{2}-9 x+7)\)

Step 5 ：Simplify the above expression to get \(f(x+h)-f(x) = h^{2}+2hx-9h\)

Step 6 ：Divide \(f(x+h)-f(x)\) by \(h\) to get the difference quotient \(\frac{f(x+h)-f(x)}{h} = h + 2x - 9\)

Step 7 ：Final Answer: The difference quotient of the function \(f(x)=x^{2}-9 x+7\) is \(\boxed{h + 2x - 9}\)