Simplify-
`(x-y)/(xy)+(y-z)/(yz)+(z-x)/(zx)`

If xy + yz + zx = 1 find (x+y)/(1-xy) + (y+z)/(1-yz) + (z + x)/(1-zx) = ?

simplify- (((x+y)^2-xy)/((y-z)(z-x)))+(((y+z)^2-yz)/((z-x)(x-y)))+(((z+x)^2-zx)/((x-y)(y-z)))

Simplify- (x-y-z)(x^2+y^2+z^2+xy-yz+zx)

If x^(3)+y^(3)+z^(3)=3xyz and x+y+z=0 , then the value of ((x+y)^(2))/(xy)+((y+z)^(2))/(yz)+((z+x)^(2))/(zx) is

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

If x + y + z = 0 , then the value of (x^2)/(yz) + (y^2)/(zx) + (z^2)/(xy) is: