F is a field.. Using field arithmetic and the definition of the symbol a/b show that if a,b,x,y are elements of F with b,y not =0 then
a/b + x/y = (ay+bx)/by

I don't even know where to start with this one, so any help anyone you can offer would be greatly appreciated!

2. Originally Posted by amm345
F is a field.. Using field arithmetic and the definition of the symbol a/b show that if a,b,x,y are elements of F with b,y not =0 then
a/b + x/y = (ay+bx)/by

I don't even know where to start with this one, so any help anyone you can offer would be greatly appreciated!
By definition, $a/b = ab^{-1}$.
Let $X = ab^{-1} + xy^{-1}$ then $(by)X = ab^{-1}(by) + xy^{-1}(yb)$.
Therefore, $byX = ay + bx \implies X = (ay+bx)(by)^{-1} = (ay+bx)/(by)$.