Question

Solve $\frac{(x-y{)}^3+{(y-z)}^3+{(z-x)}^3}{9(x-y)(y-z)(z-x)}=?$

Answer 1

$\frac{(x-y{)}^3+{(y-z)}^3+{(z-x)}^3}{9(x-y)(y-z)(z-x)}$
Let us Assume that $A=x-y,B=y-z,C=z-x$ or $A+B+C=0$
$A^3+B^3+C^3=3ABC$
$\frac{3(x-y)+(y-z)+(z-x)}{9(x-y)(y-z)(z-x)}$
$=\frac{1}{3}$