已知Y=X平方-2X+1/X平方-1除以X平方-X/X+1-1/X+1试说明在代数试有意义的条件下,不论X为何值,Y的值不变

y=[(x^2-2x+1)/(x^2-1)]/[(x^2-x)/(x+1)]-1/x+1
=[(x-1)^2/(x+1)(x-1)]/[x(x-1)/(x+1)]-1/x+1
=[(x-1)/(x+1)]*[(x+1)/x(x-1)]-1/x+1
=1/x-1/x+1
=1
所以无论x取何值,Y的值不变