smc

First, note that $y\ne \pm a$ because that would make the denominator $0$. Create common denominators in the complex fraction. $$\frac{\frac{a^2-ay}{a^2-y^2}+\frac{ay+y^2}{a^2-y^2}}{\frac{ay-y^2}{a^2-y^2}-\frac{a^2+ay}{a^2-y^2}}$$ $$\frac{\frac{a^2+y^2}{a^2-y^2}}{\frac{-a^2-y^2}{a^2-y^2}}$$ Since $a\ne 0$, $a^2+y^2>0$, so no other restrictions need to be made. $$\frac{a^2+y^2}{a^2-y^2}\cdot \frac{a^2-y^2}{-a^2-y^2}$$ $$\frac{a^2+y^2}{-(a^2+y^2)}$$ $$-1$$ The expression (with suitable restrictions) simplifies to $-1$, so the answer is $\boxed{\text{all but two real values of }y}$.