$5 \cdot 1$ Given the following equations:
I. $y=x-2$.
II. $y=\frac{x^{2}-4}{x+2}$.
III. $(x+2) y=x^{2}-4$.

Which of the following represent the same graph?
(A) I and II.
(B) I and III.
(C) II and III.
(D) I, II, and III.
(E) None represent the same graph.
(43rd American High School Mathematics Examination, 1992)
[Solution] For II, $x \neq-2$, which means its graph is the line $y=x-2$ excluding the point $(-2,-4)$.
For III, its graph consists of two lines
$$
x+2=0 \text { and } y=x-2 \text {. }
$$

Clearly, the graphs of I, II, and III are all different.
Therefore, the answer is $(E)$.