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Define associativity

It is associative i did it by verifying LHS=RHS
Although intuition pointed it right away

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 \((x*y)*z=\frac{(x+y)+z}{1+(xy)z}=\frac{x+(y+z)}{1+x(yz)}=x*(y*z).\)

You're welcome.