解关于x的方程x+a+b/c+x+b+c/a+x+c+a/b=-3
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解关于x的方程x+a+b/c+x+b+c/a+x+c+a/b=-3
解关于x的方程x+a+b/c+x+b+c/a+x+c+a/b=-3
解关于x的方程x+a+b/c+x+b+c/a+x+c+a/b=-3
题目是(x+a+b)/c+(x+b+c)/a+(x+c+a)/b=-3 吧
x/c +a/c +b/c + x/a + b/a +c/a + x/b +c/b +a/b =-3 去括号
(1/a +1/b +1/c )* x = -(3+ a/c +b/c + b/a +c/a +c/b +a/b) 移项
(1/a +1/b +a/c) *x = -[(1+a/c +b/c) +(1+ b/a +c/a ) +(1+c/b +a/b)]
(1/a +1/b +a/c) *x = -[(a+b+c)/c +(a+b+c )/a +(a+b+c )/b]
(1/a +1/b +a/c) *x = -[1/c +1/a +1/b] *(a+b+c)
x=-a-b-c
两边加3得
(x+a+b+c)(1/a+1/b+1/c)=0
所以x=-(a+b+c)
x/c +a/c +b/c + x/a + b/a +c/a + x/b +c/b +a/b =-3
(1/a +1/b +1/c )* x = -(3+ a/c +b/c + b/a +c/a +c/b +a/b)
(1/a +1/b +a/c) *x = -[(1+a/c +b/c) +(1+ b/a +c/a ) +(1+c/b +a/b)]
全部展开
x/c +a/c +b/c + x/a + b/a +c/a + x/b +c/b +a/b =-3
(1/a +1/b +1/c )* x = -(3+ a/c +b/c + b/a +c/a +c/b +a/b)
(1/a +1/b +a/c) *x = -[(1+a/c +b/c) +(1+ b/a +c/a ) +(1+c/b +a/b)]
(1/a +1/b +a/c) *x = -[(a+b+c)/c +(a+b+c )/a +(a+b+c )/b]
(1/a +1/b +a/c) *x = -[1/c +1/a +1/b] *(a+b+c)
x=-a-b-c
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