1992 AHSME Problem 14

Which of the following equations have the same graph?

I.\quad y=x-2 \qquad II.\quad y=\frac{x^2-4}{x+2}\qquad III.\quad (x+2)y=x^2-4

\begin{array}{l} \text{(A) I and II only} \quad \text{(B) I and III only} \quad \text{(C) II and III only} \quad \text{(D) I,II,and III} \quad \\ \text{(E) None. All of the equations have different graphs} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.