A*B等于A+B分之AB,那么(A*B)*C是否等于A*(B*C)?
问题描述：
A*B等于A+B分之AB,那么(A*B)*C是否等于A*(B*C)?
题中星号不是乘号,代表的是一种定义新运算.题中乘号均省略.
答
答：A*B=AB/(A+B)则有：(A*B)*C=[AB/(A+B)]*C=[ABC/(A+B)]/[AB/(A+B)+C]=ABC/[AB+(A+B)C]=ABC/(AB+AC+BC)A*(B*C)=A*[BC/(B+C)]=[ABC/(B+C)]/[A+BC/(B+C)]=ABC/[A(B+C)+BC]=ABC/(AB+AC+BC)=(A*B)*C所以：(A*B)*C=A*(B...