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

(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))

(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 : "

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)))

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)) .

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))

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))

Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(x-y)(y-z)(z-x)(x+y+z)(x^2+y^2+z^2)dot

Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(x-y)(y-z)(z-x)(x+y+z)(x^2+y^2+z^2)dot