In Charles Pinter's A Book of Abstract Algebra, Chapter 2: Operations, Section B. Properties of Operations, Question 7 part ii, an operation * is defined on the set of real numbers: $x * y = \frac{xy}{x+y+1} $ I need to find if it is associative, so: $$ \begin{align*} x*(y*z) &= x* \frac{yz}{y+z+1} \\\\ &= \frac{\frac{xyz}{y+z+1}}{x+\frac{yz}{y+z+1}+1} \\\\ &= \frac{\frac{xyz}{y+z+1}}{\frac{xy+xz+x+yz+y+z+1}{y+z+1}} \\\\ &= \frac{xyz}{xy+xz+yz+x+y+z+1} \\\\ \end{align*} $$
Then the same answer for $(x*y)*z$. This is not the same as the answer given at the end: Answer at back
What have I overlooked?
