`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=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 +y+ z=xyz , 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) .

Prove that |{:(x^2,y^2,z^2),((x+1)^2,(y+1)^2,(z+1)^2),((x-1)^2,(y-1)^2,(z-1)^2):}|=-4(x-y)(y-z)(z-x)

If x+y+z=x y z 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)dot

If x+y+z=x y z 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)dot

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,show 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+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))

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)|=(x-y)(y-z)(z-x)

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