Proving Normality of [G,G] in G: A Commutator Question

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Perhaps someone will help me in this.
I need to prove that the group [G,G] of elements of the form gh g^{-1}h^{-1} where g,h in G, is normal in G, i.e if k is in G, then kghg^{-1}h^{-1}k^{-1}=aba^{-1}b^{-1} for some a,b in G.
I tried writing it as kghkk^{-1}g^{-1}h^{-1}k^{-1}, but here is where my attmempt run down the mill, as in not successful.
Any hints?
 
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Conjugate two elements g,h by the same element and compute the commutator.
 
Ok, thanks.
 

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