Method of characteristics and general solution for partial differential equations

Find the general solution of the linear equation , x²u_{x +} y²u_y = (x+y)u .

I found out the first constant C₁ = x^-1 - y^-1 ,

using dx/x² = dy/y² = du/(x+y)u. (1)

According to my book, the second constant C₂ = (x -y)/u , using (dx -dy)/ (x²-y²) = du/(x+y)u.

I don't understand how did they derive (dx -dy)/(x² - y²) from equation (1)?

Can someone please help me out with this ?