(2a-b-c)/(a-b)(a-c)+(2b-c-a)/(b-c)(b-a)+(2c-a-b)/(c-b)(c-a)
=(a-b+a-c)/(a-b)(a-c)+(b-c+b-a)/(b-c)(b-a)+(c-b+c-a)/(c-b)(c-a)
=1/(a-c)+1/(a-b)+1/(b-a)+1/(b-c)+1/(c-a)+1/(c-b)
=1/(a-c)-1/(a-c)+1/(a-b)-1/(a-b)+1/(b-c)-1/(b-c)
=0
(2a-b-c)/(a-b)(a-c)+(2b-c-a)/(b-c)(b-a)+(2c-a-b)/(c-b)(c-a)
=(a-b+a-c)/(a-b)(a-c)+(b-c+b-a)/(b-c)(b-a)+(c-b+c-a)/(c-b)(c-a)
=1/(a-c)+1/(a-b)+1/(b-a)+1/(b-c)+1/(c-a)+1/(c-b)
=1/(a-c)-1/(a-c)+1/(a-b)-1/(a-b)+1/(b-c)-1/(b-c)
=0