解一道初一的分式方程

题目

解一道初一的分式方程
（x+1)/(x+2)+(x+6)/(x+7)=(x+2)/(x+3)+(x+5)/(x+6)
求x的值

答案

（x+1)/(x+2)+(x+6)/(x+7)=(x+2)/(x+3)+(x+5)/(x+6)
(x+2-1)/(x+2)+(x+7-1)/(x+7)=(x+3-1)/(x+3)+(x+6-1)/(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)
(x+7+x+2)/(x+2)(x+7)=(x+6+x+3)/(x+3)(x+6)
(2x+9)/(x+2)(x+7)=(2x+9)/(x+3)(x+6)
所以2x+9=0
x=-4.5
经检验,x=-4.5是原方程得解