Compute the derivative of the given function in two different ways. $\displaystyle{ h(x) = \frac{{x^{3}+3x^{2}}}{{2x^{2}}} }$

1. Use the Quotient Rule, $\displaystyle\left[\frac{f}{g}\right]' = \frac{g\cdot f' - f \cdot g'}{g^2}$. (Fill in each blank, then simplify.)
   \(h'(x) = \)

   \(\Big(\)\( \Big) \cdot \Big(\)\(\Big) - \Big(\)\(\Big) \cdot \Big(\)\(\Big)\)

   \( = \)
2. Use algebra first to simplify $h$, then differentiate without the Quotient Rule.
   $h'(x) =$