Which of the following equations have the same graph?
$I.\quad y=x-2 \qquad II.\quad y=\frac{x^2-4}{x+2}\qquad III.\quad (x+2)y=x^2-4$
$\text{(A) I and II only} \quad \text{(B) I and III only} \quad \text{(C) II and III only} \quad \text{(D) I,II,and III} \quad \\ \text{(E) None. All of the equations have different graphs}$
The equations differ at $x=-2$. The graph of $I$ would contain the point $(-2, -4)$; $-2$ is undefined in the graph of $II$ because it gives a denominator of $0$; and the graph of $III$ contains the whole the vertical line $x = -2$ as for any $y$ value, the equation still satisfies $0 = 0$. So the answer is ${E}$.