(x+1)/(x-2)+1/(x+1)=1
(x-2+3)/(x-2)+1/(x+1)=1
(x-2)/(x-2)+3/(x-2)+1/(x+1)=1
1+3/(x-2)+1/(x+1)=1
3/(x-2)+1/(x+1)=0
3(x+1)/(x+1)(x-2)+(x-2)/(x+1)(x-2)=0
[3(x+1)+(x-2)]/(x+1)(x-2)=0
[3x+3+x-2]/(x+1)(x-2)=0
(4x+1)/(x+1)(x-2)=0
4x+1=0
x=-1/4
经检验x=-1/4是方程的解