初一 数学 急 请详细解答,谢谢! (13 10:40:40)

a+b+c=0
所以a+b=-c, a+c=-b, b+c=-a

a(1\b+1\c)+b(1\a+1\c)+c(1\a+1\b)
=a\b+a\c+b\a+b\c+c\a+c\b
=(b+c)\a+(a+c)\b+(a+b)\c
=(-a\a)+(-b\b)+(-c\c)
=-1-1-1
=-3

原式=a(1/a+1/b+1/c)+b(1/a+1/b+1/c)+c(1/a+1/b+1/c)-3
=(a+b+c)(1/a+1/b+1/c)-3=-3

原式= (a+c)/b + (a+b)/c + (b+c)/a
= (-b/b) + (-c/c) + (-a/a)
= -3

a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)
=a(b+c)/bc+b(a+c)/ac+c(a+b)/ab
=-a^2/bc-b^2/ac-c^2/ab
=-(a^3+b^3+c^3)/abc
=-(a^3+b^3+c^3-3abc)/abc+3abc/abc
=-(a+b+c)(a^2+b^2+c^2-ab-bc-ca)/abc+3
=0+3
=3

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

=a/b+a/c+b/a+b/c+c/a+c/b

=(a+b)/c+(b+c)/a+/()a+c/b

=-a/a-b/b-c/c

=-3

得：(a/b+a/c)+(b/c+b/a)+(c/a+c/b)
=a/b+a/c+b/c+b/a+c/a+c/b
=(a/b+c/b)+(a/c+b/c)+(b/a+c/a)
=(a+c)/b+(a+b)/c+(b+c)/a
由因为 A+B=-C，A+C=-B，B+C=-A