解这个方程：1/(x+1)=(1-x)/(x-2)+2

1/(x+1)=(1-x)/(x-2)+2
1=(1-x)(1+x)/(x-2)+2(1+x)
1=(1-x^2)/(x-2)+2(1+x)
1(x-2)=(1-x^2)+2(1+x)(x-2)
x-2=1-x^2+2(x-2+x^2-2x)
x-2=1-x^2+2x-4+2x^2-4x=x^2-2x-3
x^2-3x-1=0
x=(3+(-)(sqr(13))/2

sqr表示“根号”

1/(x+1)=(1-x)/(x-2)+2
1/(x+1)=(1-x+2x-4)/(x-2)
1/(x+1)=(x-3)/(x-2)
(x-2)=(x+1)(x-3)
x^2-2x-3=x-2
x^2-3x-1=0
x=(3±√13)/2
x1=(3+√13)/2
x2=(3-√13)/2
经检验，他们都是原方程的解