Question

解方程：(x+1)/(x+2)+（x+6)/(x+7)=(x+2)/(x+3)+(x+5)/(x+6)

步骤！！！

Answer 1

解:(1-1/x+2)+(1-1/x+7)=(1-1/x+3)+(1-1/x+6)
整理得:1/x+2 + 1/x+7 = 1/x+3 + 1/x+6
1/x+2 - 1/x+3 = 1/x+6 - 1/x+7
1/(x+2)(x+3) = 1/(x+6)(x+7)
(x+6)(x+7)=(x+2)(x+3)
所以 x= -9/2

Answer 2

（x+1)/(x+2)+(x+6)/(x+7)=(x+2)/(x+3)+(x+5)/(x+6)
1-1/(x+2)+1-1/(x+7)=1-1/(x+3)+1-1/(x+6)
-1/(x+2)-1/(x+7)=-1/(x+3)-1/(x+6)
1/(x+2)+1/(x+7)=1/(x+3)+1/(x+6)
1/(x+2)-1/(x+3)=1/(x+6)-1/(x+7)
(x+3-(x+2))/(x+2)(x+3)=(x+7-(x+6))/(x+6)(x+7)
1/(x+2)(x+3)=1/(x+6)(x+7)
(x+2)(x+3)=(x+6)(x+7)
x^2+5x+6=x^2+13x+42
8x=-36
x=-9/2
经检验，X=-9/2是方程的解。

Answer 3

环境开会

Answer 4

x=4