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. \[ f(x)=2 x^{2}-x-1 \] \[ \frac{f(x+h)-f(x)}{h}=\square \text { (Simplify your answer.) } \]

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

Step 2 ：Substitute \(x+h\) into the function to get \(f(x+h)=2(x+h)^{2}-(x+h)-1\)

Step 3 ：Simplify to get \(f(x+h)=2x^{2}+4hx+2h^{2}-x-h-1\)

Step 4 ：Subtract the function at \(x\) from \(f(x+h)\) to get \(f(x+h)-f(x)=(2x^{2}+4hx+2h^{2}-x-h-1)-(2x^{2}-x-1)\)

Step 5 ：Simplify to get \(f(x+h)-f(x)=4hx+2h^{2}-h\)

Step 6 ：Divide by \(h\) to get the difference quotient \(\frac{f(x+h)-f(x)}{h}=4x+2h-1\)

Step 7 ：Final Answer: The difference quotient of the function \(f(x)=2 x^{2}-x-1\) is \(\boxed{4x + 2h - 1}\)