TITLE: if $f\left(x+y,\frac{y}{x}\right)= x^2-y^2$ then $f(x,y)=?$
QUESTION [6 upvotes]: So, I have to find $f(x,y)$ if the following holds: 
$$f\left(x+y,\frac{y}{x}\right)= x^2-y^2$$ 
I thought about replacing $x+y=X$, and $y/x=Y$, but now where do I replace this $x$ and $y$ that I've found?

REPLY [7 votes]: Set $X=x+y,Y=\frac{y}{x}$. Can you solve for $x,y$ as functions of $X,Y$?