(2a-b-c)/(a^2-ab-ac+bc)=[(a-b)+(a-c)]/(a-b)(a-c)=1/(a-b)+1/(a-c)
(2b-c-a)/(b^2-bc-ab+ac)=[(b-a)+(b-c)]/(b-a)(b-c)=1/(b-a)+1/(b-c)(2c-a-b)/(c^2-ac-bc+ab)=[(c-a)+(c-b)]/(c-a)(c-b)=1/(c-a)+1/(c-b)原式=1/(a-b)+1/(a-c)+1/(b-a)+1/(b-c)+1/(c-a)+1/(c-b) =1/(a-b)+1/(b-a)+1/(a-c)+1/(c-a)+1/(b-c)+1/(c-b) =0 2.原式=(b-c)^2/(a-b)(a-c)(b-c)+(c-a)^2/(b-a)(c-a)(b-c)+(a-b)^2/(c-a)(c-b)(a-b) =(b-c)^2/(a-b)(a-c)(b-c)+(c-a)^2/(a-b)(a-c)(b-c)+(a-b)^2/(a-c)(b-c)(a-b) =2(a^2+b^2+c^2-ab-ac-bc)/(a-b)(a-c)(b-c) 3.1/x-1/y=(y-x)/xy=3 ∴x-y=-3xy 原式=(3x+5xy-3y)/(x-3xy-y)=(-9xy+5xy)/(-3xy-3xy)=2/3 4.(x-2)^3-(x-1)^2+1=(x-2)^3-x(x-2)=(x-2)(x^2-5x+4) ∵x^2-5x-2003=0 ∴x^2-5x+4=2007 原式=(x-2)*2007/(x-2)=2007 5.原式=a/b+a/c+b/c+b/a+c/a+c/b =(a+c)/b+(a+b)/c+(b+c)/a ∵a+b+c=0 ∴a+c=-b,a+b=-c,b+c=-a ∴(a+c)/b+(a+b)/c+(b+c)/a=-1+-1+-1=-3