百度作业网问一道初中的数学化简题……急!有图!
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/08/18 12:57:42
问一道初中的数学化简题……急!有图!
(a+1)/(a-b)(a-c) + (b+1)/(b-a)(b-c) + (1+c)/(c-a)(c-b)
=(a+1)/(a-b)(a-c) + (b+1)/-(a-b)(b-c) + (1+c)/[-(a-c)]×[-(b-c)]
=(a+1)/(a-b)(a-c) - (b+1)/(a-b)(b-c) + (1+c)/(a-c)(b-c)
=(a+1)(b-c)/(a-b)(a-c) (b-c) - (b+1)(a-c)/(a-b)(b-c)(a-c) + (1+c)(a-b)/(a-c)(b-c)(a-b)
=((a+1)(b-c)-(b+1)(a-c)+(1+c)(a-b)) /(a-b)(a-c) (b-c)
=(ab-ac+b-c-ab+bc-a+c+a-b+ac-bc) /(a-b)(a-c) (b-c)
=((ab-ab)+(ac-ac)+(bc-bc)+(a-a)+(b-b)+(c-c)) /(a-b)(a-c) (b-c)
=0 / (a-b)(a-c) (b-c)
=0
=(a+1)/(a-b)(a-c) + (b+1)/-(a-b)(b-c) + (1+c)/[-(a-c)]×[-(b-c)]
=(a+1)/(a-b)(a-c) - (b+1)/(a-b)(b-c) + (1+c)/(a-c)(b-c)
=(a+1)(b-c)/(a-b)(a-c) (b-c) - (b+1)(a-c)/(a-b)(b-c)(a-c) + (1+c)(a-b)/(a-c)(b-c)(a-b)
=((a+1)(b-c)-(b+1)(a-c)+(1+c)(a-b)) /(a-b)(a-c) (b-c)
=(ab-ac+b-c-ab+bc-a+c+a-b+ac-bc) /(a-b)(a-c) (b-c)
=((ab-ab)+(ac-ac)+(bc-bc)+(a-a)+(b-b)+(c-c)) /(a-b)(a-c) (b-c)
=0 / (a-b)(a-c) (b-c)
=0