计算:(a-b)(a-c)分之a+(b+c)(b-a)分之b+(c-a)(c-b)分之c_数学解答

计算:(a-b)(a-c)分之a+(b+c)(b-a)分之b+(c-a)(c-b)分之c

人气：370 ℃　时间：2020-02-02 18:26:12

解答

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