x/(xy+z+1)+y/(yz+x+1)+/(xz+y+1)

Question

x/(xy+z+1)+y/(yz+x+1)+/(xz+y+1)

Answer 1

1)xy+z+1=(xy+1)(z+1)-1=(xy+1)(z+xyz)-1=z(xy+1)(xy+1)-1
2)xy+z+1=(xy+1)(z+1)-1=(xy+xyz)(z+1)-1=xy(z+1)(z+1)-1
3)z(xy+1)(xy+1)-1=xy(z+1)(z+1)-1
z(xy+1)(xy+1)-xy(z+1)(z+1)=0
(√z(xy+1)-√xy(z+1))(√z(xy+1)+√xy(z+1))=0
解得：√z(xy+1)-√xy(z+1)=0
√z(xy+1)+√xy(z+1)=0
2√z(xy+1)=0
x、y、z≠0
xy=-1
z=-1
4）yz+x+1
按上述步骤可求得x=-1,y=1
5）x=-1,y=1,z=-1代入
x/(xy+z+1)+y/(yz+x+1)+z/(xz+y+1)= 1-1-1/3=-1/3