已知:xyz=1,求(x/(xy+x+1))+(y/(yz+y+1))+(z/(xz+z+1))的值.我用(())来代表中括号和小括号.

Question

已知:xyz=1,求(x/(xy+x+1))+(y/(yz+y+1))+(z/(xz+z+1))的值.
我用 (())来代表中括号和小括号.

Answer 1

因为 xyz-1,所以 y/(yz+y+1) (分子分母同时乘以x)=xy/(xyz+xy+x) (xyz=1)=xy/(xy+x+1)同理,在z/(xz+z+1)的分子分母上同时乘以xy得到 z/(xz+z+1)=xyz/(x^2yz+xyz+xy)=1/(xy+x+1)所以 原式=x/(xy+x+1)+xy/(xy+x+1)+1/(...