Question

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

如题~

Answer 1

(x+1/x+2)-(x+2/x+3)=(x+5/x+6)-(x+6)/(x+7)
(x+1/x+2)+(x+6)/(x+7)=(x+5/x+6)+(x+2/x+3)
(x+1/x+2)-1+(x+6)/(x+7)-1=(x+5/x+6)-1+(x+2/x+3)-1
(x+1-x-2/x+2)+(x+6-x-7)/(x+7)=(x+5-x-6/x+6)+(x+2-x-3/x+3)
-1/(x+2)-1/(x+7)=-1/(x+6)-1/(x+3)
1/(x+2)+1/(x+7)=1/(x+6)+1/(x+3)
通分
(2x+9)/(x²+9x+14)=(2x+9)/(x²+9x+18)
(2x+9)[1/(x²+9x+14)-1/(x²+9x+18)]=0
x²+9x+14≠x²+9x+18
所以1/(x²+9x+14)-1/(x²+9x+18)≠0
2x+9=0
x=-9/2
分式方程要检验
经检验，x=-9/2是方程的解