Question

if x+y+z=0,then prove that x y z/(x+y) (y+z) (z+x) = -1

Answer 1

if x+y+z=0
then x+y=-z
y+z=-x
x+z=-y
x y z/(x+y)(y+z)(z+x)
=x y z/(-z)(-y)(-x)

= x y z/-(x y z)
= -1