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I'm quite new to Mathematica and stuck at a point, where I have searched for hours to find a solution, but there seems no way out.

Let's say we have two functions,

f1[x_,y_]=x+y

f2[x_,y_]=x*y

How can a build a function f3, which is e.g. the sum of the other functions f1 and f2, i.e. f3[x_, y_]=x+y+x*y, but without copy&paste, but with direct dependency on f1 and f2?

With f3=f1[x,y]+f2[x,y], the functional dependency on x and y is missing. I need a f3, which also has the same input arguments as f1 and f2 (namely x and y).

With f3[x_,y_]==f1[x,y]+f2[x,y] the functional dependency on the parameters is also not working.

Thanks you for your help,

I'm really desperate :(