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what's the easiest way to determine whether the binary operation * is associative, if * is defined by \(x*y=\frac{x+y}{1+xy} \)

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Define associativity
x*(y*z)=(x*y)*z ... if it's associative, then the right hand side should be equal to the left hand side
It is associative i did it by verifying LHS=RHS Although intuition pointed it right away

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well is that the easiest way...? i was thinking maybe there's a faster method
It clearly follows from the associativity of addition and multiplication.
what do u mean by that?
I mean \((x*y)*z=\frac{(x+y)+z}{1+(xy)z}=\frac{x+(y+z)}{1+x(yz)}=x*(y*z).\)
ohhh okay, well i was doing some weird workings but the answer was quite obvious right from the beginning :) thanks
You're welcome.

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