1/(b-a)(b-c)+1/(c-a)(c-b)+1/(a-b)(a-c)
=1/(a-b)(a-c)+1/(b-a)(b-c)+1/(c-a)(c-b)
=[(b-c)-(a-c)+(a-b)]/[(a-b)(a-c)(b-c)]
=0/[(a-b)(a-c)(b-c)]
=0
1/(b-a)(b-c)+1/(c-a)(c-b)+1/(a-b)(a-c)
=1/(a-b)(a-c)+1/(b-a)(b-c)+1/(c-a)(c-b)
=[(b-c)-(a-c)+(a-b)]/[(a-b)(a-c)(b-c)]
=0/[(a-b)(a-c)(b-c)]
=0