If $h(2)=3$ and $h^{\prime}(2)=-4$, find \[ \left.\frac{d}{d x}\left(\frac{h(x)}{x}\right)\right|_{x=2} \]

Step 1 ：The problem is asking for the derivative of the function \(\frac{h(x)}{x}\) evaluated at \(x=2\).

Step 2 ：We can use the quotient rule for differentiation, which states that the derivative of a quotient \(\frac{u}{v}\) is given by \(\frac{vu' - uv'}{v^2}\). Here, \(u=h(x)\) and \(v=x\).

Step 3 ：We know that \(h(2)=3\) and \(h'(2)=-4\). We can substitute these values into the quotient rule to find the derivative at \(x=2\).

Step 4 ：The derivative of the function \(\frac{h(x)}{x}\) at \(x=2\) is \(\boxed{-2.75}\).