Early Abstract Algebra Problem - Pinter's Textbook

[physicsforum7]

Homework Statement

This problem is from Charles C. Pinter's A Book of Abstract Algebra, Second Edition. The problem is B7 of Chapter 2.Show that the operation * is either associative or not.

x*y=\frac{xy}{x+y+1} This problem seems simple to me: I keep arriving at YES for an answer; more specifically,

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

However, the solution in the back claims that the answer is NO, the operation is not associative. More specifically,

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

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

After working the problem through several times, I'm pretty sure this is a mistake in the book. But I would greatly appreciate feedback so that I can be sure I'm not doing something terribly wrong.

Thank you very much.

 

[micromass]

I agree with you. The operation seems to be associative.

 

[funwalla]

I also get the same result.

 

[HallsofIvy]

But surely your text does not "Show that the operation * is either associative or not."
Every operation is "either associative or not"!

Better wording would be "Determine whether the operation * is either associative or not."