Find dy/dx (or just call it y') by implicit differentiation.

tan(x/y) = x + y

I see the answer but I need to understand it. Can someone explain it well plz? I did the following so far:

1) Derivative of tan(x/y) = [sec(x/y)]^2 * [(y-xy')/y^2]
is equal to
2) Derivative of x + y = 1 + y'

Is this right so far? If so then I'm just having trouble simplifying the way the book does I guess.