a/x=(y+z)/yz b/y=(z+x)/zx c/z=(x+y)/xy
a=x(y+z)/yz b=y(z+x)/zx c=z(x+y)/xy
1/(a+1)+1/(b+1)+1/(c+1)
= 1/[(x(y+z)/yz) +1]+1/[y(z+x)/zx+1]+1/[z(x+y)/xy+1]
=yz/(xy+xz+yz)+xz/(xy+xz+yz)+xy/(xy+yz+xy)
=(yz+xz+xy)/(xy+yz+xy)
=1
a/x=(y+z)/yz b/y=(z+x)/zx c/z=(x+y)/xy
a=x(y+z)/yz b=y(z+x)/zx c=z(x+y)/xy
1/(a+1)+1/(b+1)+1/(c+1)
= 1/[(x(y+z)/yz) +1]+1/[y(z+x)/zx+1]+1/[z(x+y)/xy+1]
=yz/(xy+xz+yz)+xz/(xy+xz+yz)+xy/(xy+yz+xy)
=(yz+xz+xy)/(xy+yz+xy)
=1