1.8 Let $a$ be a real number not equal to 0. In which of the following cases does
$$
\frac{\frac{a}{a+y}+\frac{y}{a-y}}{\frac{y}{a+y}-\frac{a}{a-y}}=-1 .
$$
(A) All real numbers except two real values of $y$.
(B) Only two real values of $y$.
(C) All real values of $y$.
(D) 36.5 .
(E) 36 .
(14th American High School Mathematics Examination, 1963)
[Solution] If $y \neq \pm a$, then the left side of the given equation can be transformed as
$$
\frac{a^{2}-a y+a y+y^{2}}{a y-y^{2}-a^{2}-a y}=\frac{a^{2}+y^{2}}{-\left(a^{2}+y^{2}\right)}=-1 \text {. }
$$

Therefore, the correct choice is $(A)$.