When going through a solution concerning a differential equation we have the following expression:
$(1-\frac{x^2}{y^2})\frac{dy}{dx} + \frac{2x}{y} = 0$
and then its said to note that:
$ \frac{d}{dx}(\frac{x^2}{y}+y)=\frac{2x}{y}-\frac{x^2}{y^2}\frac{dy}{dx} + \frac{dy}{dx} = (1-\frac{x^2}{y^2})\frac{dy}{dx} + \frac{2x}{y}$
so that we later can use the expression to the left, but I don't really understand how the $\frac{dy}{dx}$ is used here, could someone explain how ? Specifically what is going on with the $-\frac{x^2}{y^2}\frac{dy}{dx}+ \frac{dy}{dx}$ terms in the middle part.
Thanks