原式=a²/(a-b)(a-c)-b²/(a-b)(b-c)+c²/(a-c)(b-c)
=[a²(b-c)-b²(a-c)+c²(a-b)]/(a-b)(a-c)(b-c)
=[a²b-a²c-ab²+b²c+c²(a-b)]/(a-b)(a-c)(b-c)
=[ab(a-b)-c(a+b)(a-b)+c²(a-b)]/(a-b)(a-c)(b-c)
=(a-b)(a-c)(b-c)/(a-b)(a-c)(b-c)
=1