两道初中数学题（1）化简分式(x^2-1/x^2+2x+1)-(x+1/x-1)

（1）化简分式(x^2-1/x^2+2x+1)-(x+1/x-1)
=(x+1)(x-1)/(x+1)^2-(x+1)/(x-1)
=(x-1)/(x+1)-(x+1)/(x-1)
=[(x-1)^2-(x+1)^2]/(x+1)(x-1)
=-4x/(x+1)(x-1)
（2）解方程(x-1/x)-(x/x-1)=5/2
(x-1)^2-x^2=5/2x(x-1)
-2x+1=2.5x^2-2.5x
2.5x^2-0.5x-1=0
5x^2-x-2=0
x^2-x/5=2/5
(x-1/10)^2=2/5+1/100=41/100
x-1/10=(+/-)根号41/10
X1=(1+根号41)/10
X2=(1-根号41)/10
检验,X1,X2是方程的根.

X^2-1/X^2+2X+1-X+1/X-1
=(X^2-1)(X-1)-(X+1)(X^2+2X+1)/(X^2+2X+1)(X-1)
=-5X^2+3X+2/(X+1)^2*(X-1)
=(5X+2)(1-X)/(X+1)^2*(X-1)
=5X+2/X^2+2X+1