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

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

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

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

"The value of "(x^(2))/((x-y)(x-z))+(y^(2))/((y-z)(y-x))+(z^(2))/((z-x)(z-y))" is : "

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

The simplified form of x(y-z)(y+z)+y(z-x)(z+x)+z(x-y)(x+y) 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))