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## sasogeek 3 years ago 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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1. NotSObright

Define associativity

2. sasogeek

x*(y*z)=(x*y)*z ... if it's associative, then the right hand side should be equal to the left hand side

3. NotSObright

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

4. sasogeek

well is that the easiest way...? i was thinking maybe there's a faster method

5. Mr.Math

It clearly follows from the associativity of addition and multiplication.

6. sasogeek

what do u mean by that?

7. Mr.Math

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

8. sasogeek

ohhh okay, well i was doing some weird workings but the answer was quite obvious right from the beginning :) thanks

9. Mr.Math

You're welcome.

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