解方程:1/(x+5)+1/(x+8)=1/(x+6)+1/(x+7)

解方程:1/(x+5)+1/(x+8)=1/(x+6)+1/(x+7)快?!!

解:
1/(x+5)+1/(x+8)=1/(x+6)+1/(x+7)
(x+5+x+8)/[(x+5)(x+8)]=(x+6+x+7)/[(x+6)(x+7)]
(2x+13)/(x�0�5+13x+40)=(2x+13)/亩尘(x�0�5+13x+42)
由于分母x�0�5+13x+40恒≠x�0�5+13x+42,要等式成立,只有分子为或罩0,即
2x+13=0
x=-13/2

楼上搞复杂了,其实就是一步判衫耐闹断的问题,不要分类讨论。