Knowledge Check Find the difference quotient $\frac{f(x+h)-f(x)}{h}$, where $h \neq$ \[ f(x)=\frac{4}{x-1} \] Simplify your answer as much as possible. \[ \frac{f(x+h)-f(x)}{h}=\square \]

Step 1 ：Define the function \(f(x)=\frac{4}{x-1}\)

Step 2 ：Substitute \(x+h\) into the function for \(x\), getting \(f(x+h)=\frac{4}{x+h-1}\)

Step 3 ：Subtract the original function \(f(x)\) from \(f(x+h)\), resulting in \(f(x+h)-f(x)=\frac{4}{x+h-1}-\frac{4}{x-1}\)

Step 4 ：Divide the result by \(h\), getting the difference quotient \(\frac{f(x+h)-f(x)}{h}=\frac{\frac{4}{x+h-1}-\frac{4}{x-1}}{h}\)

Step 5 ：Simplify the difference quotient to get the final answer: \(\boxed{-\frac{4}{(x - 1)(h + x - 1)}}\)