The function $\displaystyle f$ has the property that $\displaystyle f(x)+f(y)= (x+y)f(xy)$ for all non-zero real numbers $\displaystyle x$ and $\displaystyle y$ . A possible rule for $\displaystyle f $ is

A. $\displaystyle f(x)=2x$

B. $\displaystyle f(x)=5-2x$

C. $\displaystyle f(x) = \frac{1}{x}$

D. $\displaystyle f(x)= e^x$

E. $\displaystyle f(x)=\ln x$

I can expand every option out. But I'm having a lazy day. Is there an easier way?