Question

已知y+z分之x =a ,x+z分之y =b ,x+y分之z =c,试求a+1分之a + b+1分之b + c+1分之c

Answer 1

因为：

a/(a+1)=[x/(y+z)]/[(x+y+z)/(y+z)]=x/(x+y+z)

b/(b+1)=[y/(x+z)]/[(x+y+z)/(x+z)]=y/(x+y+z)

c/(c+1)=[z/(x+y)]/[(x+y+z)/(x+y)]=z/(x+y+z)

所以

a/(a+1)+b/(b+1)+c/(c+1)=x/(x+y+z)+y/(x+y+z)+z/(x+y+z)=(x+y+z)/(x+y+z)=1