[x+2-5/(x-2)]/[(x-3)/(x-2)]
=[(x^2-4-5)/(x-2)]/[(x-3)/(x-2)]
=(x^2-9)/(x-2)*(x-2)/(x-3)
=(x^2-9)/(x-3)
=(x-3)(x+3)/(x-3)
=x+3
3/x-4/(x-1)=6/(x-x^2)
3/x+4/(1-x)=6/(x-x^2)
3(1-x)+4x=6
3-3x+4x=6
3+x=6
x=3
经检验x=3是方程的解
[1+(x^2-1)/(1-2x+x^2)](x-1)
=[1+(x-1)(x+1)/(x-1)^2](x-1)
=[1+(x+1)/(x-1)](x-1)
=(x-1)+(x+1)/(x-1)*(x-1)
=x-1+x+1
=2x
=2*(-3/2)
=-3