Solving the equation $- y^2 - x^2 - xy = 0$ Ok, this is really easy and it's getting me crazy because I forgot nearly everything I knew about maths!
I've been trying to solve this equation and I can't seem to find a way out.
I need to find out when the following equation is valid:
$$\frac{1}{x} - \frac{1}{y} = \frac{1}{x-y}$$
Well, $x \not= 0$, $y \not= 0$, and $x \not= y$ but that's not enough I suppose.
The first thing I did was passing everything to the left side:
$$\frac{x-y}{x} - \frac{x-y}{y} - 1 = 0$$
Removing the fraction:
$$xy - y² - x² + xy - xy = 0xy$$
But then I get stuck..
$$- y² - x² + xy = 0$$
How can I know when the above function is valid?

$x^2-xy+y^2=(x+jy)(x+j^2y)$ so $x=y(1+\sqrt{-3})/2$
