Elementary symmetric polynomial task with three variables Can anyone help me to wite this as sum or product of elementary symmetric polynomial.
$$\frac xy+\frac yx +\frac xz + \frac zx +\frac yz + \frac zy =7$$

I tried to set under one fraction, but I didn't go much far.

In the LHS of
$$x^2 y+x^2 z+x y^2+x z^2+y^2 z+y z^2= 7xyz$$
you recognize all the binary terms from the development of $(x+y+z)^3$. To complete the cube,
$$(x+y+z)^3=\color{blue}{x^3+y^3+z^3 + 3}(x^2 y+x^2 z+x y^2+x z^2+y^2 z+y z^2)\color{blue}{+6xyz}\\= x^3+y^3+z^3 +27xyz.$$
