1.(x'2+1/x+1)+[3（x+1）/(x'2+1)]=4

1.[(x^2+1)/(x+1)]+[3（x+1）/(x^2+1)]=4
t=(x^2+1)/(x+1)
t+3/t=4
t^2-4t+3=0
t=1或t=3
（x^2+1)/(x+1)=1,x^2=x,x=1或x=0
(x^2+1)/(x+1)=3 x2-3x=2 x=±√13/2+3/2
2.(2x^2-4x-3)/(x^2-2x-1)=3
2-1/(x^2-2x-1)=3
x^2-2x-3=-1
（x-1)^2=3,x=±√3+1
3.2(x^2+1/x^2)-3(x+1/x)=1
t=x+1/x ,x^2+1/x^2=t^2-2
2t^2-4-3t=1
2t^2-3t-5=0
(2t-5)(t+1)=0,t=5/2或t=-1
x+1/x=5/2,2x^2-5x+2=0,(2x-1)(x-2)=0,x=2或x=1/2
x+1/x=-1,x^2+x+1=0,无实数解
4.当m为何值时,关于x的方程m/(x^2-x-2)=x/(x+1)-(x-1)/(x-2) 的解是正数?
m/(x^-x-2)=x/(x+1)-(x-1)/(x-2)
m=x^2-2x-x^2+1
m=1-2x
x=(1-m)/2
x>0
m