\(A=\frac{x}{xy+x+1}+\frac{y}{yz+y+1}+ \frac{z}{xz+z+1}\)
\(=\frac{x}{xyz+xy+x}+\frac{y}{yz+y+1}+\frac{z}{xz+z+1}\)
\(=\frac{1}{yz+y+1}+\frac{y}{yz+y+1}+\frac{z}{xz+z+1}\)
\(=\frac{y+1}{yz+y+1}+\frac{z}{xz+z+1}\)
\(=\frac{xyz+y}{xyz+yz+y}+\frac{z}{xz+z+1 }\)
\(=\frac{xz+1}{xz+z+1}+\frac{z}{xz+z+1}\)
\(=\frac{xz+z+1}{xz+z+1}=1\)
#Carrot