`1/((x-y)^2)+1/((y-z)^2)+1/((z-x)^2)=(1/(x-y)+1/(y-z)+1/(z-x))^2`

If x,y,z are all different real numbers,then prove that (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-z)+(1)/(y-z)+(1)/(z-x))^(2)

If x+y+z=xzy , prove that : (2x)/(1-x^2) + (2y)/(1-y^2) + (2z)/(1-z^2) = (2x)/(1-x^2) (2y)/(1-y^2) (2z)/(1-z^2)

If |(x^(n),x^(n+2),x^(n+3)),(y^(n),y^(n+2),y^(n+3)),(z^(n),z^(n+2),z^(n+3))| = (x -y) (y -z) (z -x) ((1)/(x) + (1)/(y) + (1)/(z)) , then n equals

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= (4xyz)/((1-x^(2))(1-y^(2)) (1-z^(2)))

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= 4xyz/((1-x^(2))(1-y^(2)) (1-z^(2)))

The value of (x^(2)-(y-z)^(2))/((x+z)^(2)-y^(2))+(y^(2)-(x-z)^(2))/((x+y)^(2)-z^(2))+(z^(2)-(x-y)^(2))/((y+z)^(2)-x^(2)) is -1(b)0(c)1(d) None of these

D=|[(1)/(z),(1)/(z),-(x+y)/(z^(2))-(y+z)/(x^(2)),(1)/(x),(1)/(x)-(y(y+z)/(x^(2)z)),(x+2y+z)/(x)z,-(y(x+y)/(xz^(2))] then,the incorrect statement is -

If x+y+z=xyz, then value of (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))(x)/(1-x^(2))(y)/(1-y^(2))(z)/(1-z^(2))

The determinant |[ C(x,1) ,C(x,2), C(x,3)] , [C(y,1) ,C(y,2), C(y,3)] , [C(z,1) ,C(z,2), C(z,3)]|= (i) 1/3xyz(x+y)(y+z)(z+x) (ii) 1/4xyz(x+y-z)(y+z-x) (iii) 1/12xyz(x-y)(y-z)(z-x) (iv) none

Prove that : =2|{:(1,1,1),(x,y,rz),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)