The equation can be
written as
(x−aba+b−c)+(x−aca+c−b)+(x−bcb+c−a)
= 0
or x−ab−bc−caa+b+x−ab−bc−caa+c+x−ab−bc−cab+c =0
(x−ab−bc−ca)(1a+b+1a+c+1b+c)
=0
Assuming (1a+b+1a+c+1b+c)
≠ 0,
x=ab+bc+ca as the root of the equation. If, however,
(1a+b+1a+c+1b+c) = 0,
the given equation turns into an identity which holds for every value of x.