15. Given $x, y \neq 0$, and $x, y$ satisfy $xy = \frac{x}{y} = x - y$. Then the value of $x + y$ is ( ).
(A) $-\frac{3}{2}$
(B) $-\frac{1}{2}$
(C) 0
(D) $\frac{1}{2}$
(E) $\frac{3}{2}$
15.A.

From the left equation, we know $y=\frac{1}{y}$, then $y^{2}=1$. If $y=1$, the ancient equation becomes $x=x-1$, which is clearly not true. Therefore, $y=-1$. Thus, the right equation becomes $-x=x+1$. That is, $x=-\frac{1}{2}$. Therefore, $x+y=-\frac{3}{2}$.