MathCastle
Groups and FieldsHardGroups and the Group Axioms

Groups and the Group Axioms · Hard problem

Define a∗b=a+b+aba*b=a+b+ab for a,ba,b in S=Q∖{−1}S=\mathbb{Q}\setminus\{-1\}; this makes (S,∗)(S,*) a group with identity 00. Find xx such that 2∗3∗x=592*3*x=59 (where 2∗3∗x2*3*x means (2∗3)∗x(2*3)*x).