Find all possible values of $$\frac{(a+b-c)^2}{(a-c)(b-c)}+\frac{(b+c-a)^2}{(b-a)(c-a)}+\frac{(c+a-b)^2}{(c-b)(a-b)}$$
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014
Tags: value, algebra
Find all possible values of $$\frac{(a+b-c)^2}{(a-c)(b-c)}+\frac{(b+c-a)^2}{(b-a)(c-a)}+\frac{(c+a-b)^2}{(c-b)(a-b)}$$