1+a/(a-b)(a-c)+1+b/(b-c)(b-a)+1+c/(c-a)(c-b)

1+a/(a-b)(a-c)+1+b/(b-c)(b-a)+1+c/(c-a)(c-b)

(1+a)/(a-b)(a-c)+(1+b)/(b-c)(b-a)+(1+c)/(c-a)(c-b)
=(1+a)/(a-b)(a-c)-(1+b)/(b-c)(a-b)+(1+c)/(a-c)(b-c)
=[(1+a)(b-c)-(1+b)(a-c)+(1+c)(a-b)]/[(a-b)(b-c)(a-c)](通分)
=[b-c+ab-ac-a+c-ab+bc+a-b+ac-bc]/[(a-b)(b-c)(a-c)]
=0