Question

求 x/(x+1)+(x+6)/(x+7)=(x+1)/(x+2)+(x+5)/(x+6)

Answer 1

你好

x/(x+1)+(x+6)/(x+7)=(x+1)/(x+2)+(x+5)/(x+6)
[1-1/（(x+1)]+[1-1/(x+7)]=[1-1/(x+2)]+[1-1/(x+6)]
2-1/（(x+1)-1/(x+7)=2-1/(x+2)-1/(x+6)
1/(x+1)+1/(x+7)=1/(x+2)+1/(x+6)
1/(x+1)-1/(x+2)=1/(x+6)-1/(x+7)
1/(x+1)(x+2)=1/(x+6)(x+7)
(x+1)(x+2)=(x+6)(x+7)
x²+3x+2=x²+13x+42
3x+2=13x+42
-10x=40
x=-4

【数学辅导团】为您解答，不理解请追问，理解请及时选为满意回答！(*^__^*)谢谢！

Answer 2

x/(x+1)+(x+6)/(x+7)=(x+1)/(x+2)+(x+5)/(x+6）
x/(x+1)-(x+1)/(x+2)=(x+5)/(x+6)-(x+6)/(x+7)
(x+1)(x-x-2)=(x+6)(x+5-x-7)
x+1=x+6 不成立。所以原方程无解

Answer 3

(x+1-1)/(x+1)+(x+7-1)/(x+7)=(x+2-1)/(x+2)+(x+6-1)/(x+6)
1-1/(x+1)+1-1/(x+7)=1-1/(x+2)+1-1/(x+6)
1/(x+1)-1/(x+2)=1/(x+6)-1/(x+7)
通分化解得：
1/(x+1)(x+2)=1/(x+6)(x+7)
10x=-40
x=-4