解答

$${y=\frac{x^3+1}{x-1}}$$

$$\begin{eqnarray*} y&=&\frac{(x^3+1)'(x-1)-(x^3+1)(x-1)'}{(x-1)^2}\\ &=&\frac{3x^2(x-1)-(x^3+1)}{(x-1)^2}\\ &=&\frac{2x^3-3x^2-1}{(x-1)^2} \end{eqnarray*}$$