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Math Help - Proof Using Field Arithmetic-- Please Help!

  1. #1
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    Proof Using Field Arithmetic-- Please Help!

    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!
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    Quote Originally Posted by amm345 View Post
    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).
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