Question

先化简，再求值：（1/x-1）-(2/x^2-1),其中x=-2 先化简，再求值：（x/x^2-1）[(x-1/x)-2],其中x=2

Answer 1

（1/x-1）-(2/x^2-1)=（1/x-1）-(2/x^2-2)-1=（1/x-1)-2(1/x+1)(1/x-1)-1=(1/x-1)[1-2(1/x+1)]-1
=(1/x-1)(-2/x-1)-1 代入(-2/x-1)可得0 故整式结果为-1
（x/x^2-1）[(x-1/x)-2]=[(1-x)(x^2-1-2x)]/x^2=[(1-x)[(x-1)^2-2]]/x^2
代值x=2得-1*-1/4=1/4

Answer 2

（1/x-1）-(2/x^2-1)
=(x+1)/[(x+1)(x-1)]-2/[(x+1)(x-1)]
=(x+1-2)/[(x+1)(x-1)]
=(x-1)/[(x+1)(x-1)]
=1/(x+1)
x=-2
（1/x-1）-(2/x^2-1)
=1/(-2+1)=-1

[x/(x^2-1)] {[(x-1)/x]-2}
={x/[(x+1)(x-1)]} [(x-2x-1)/x] 约去x
=-(x+1)/[(x+1)(x-1)]
=-1/(x-1)
=1/(1-x)

x=2
[x/(x^2-1)] {[(x-1)/x]-2}=1/(1-2)=-1

Answer 3

1，-3/2-(-1/2)

Answer 4

(1)1/x-2/x^2=-1
(2) -1/x-1=-1