Is the operation $x*y=xy/(x+y+1)$ associative or not?

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This questions is from Charles C. Pinter's "A Book Of Abstract Algebra, Second Edition". This is the 7th question of Chapter 2 on page 24. In the selected answers section it says it is not associative but I have tried twice and keep on getting that it is associative. The given answers are $(x*y)*z = xyz(x+y+1)/(x+y+z+xy+xz+yz+1)$ and $x*(y*z) = xyz(y+z+1)/(x+y+z+xy+xz+yz+1)$

My answer is $(x*y)*z = x*(y*z) = xyz/(x+y+z+xy+xz+yz+1)$

Any help would be appreciated, thanks.