Question

先化简，再求值：(1/（x+1）+（x^2-2x+1）/（x^2-1)/（x-1）/（x+1）,其中x=3

【1/（x+1）+（x^2-2x+1）/（x^2-1)】/（x-1）/（x+1）

Answer 1

1/（x+1）+（x^2-2x+1）/（x^2-1)/（x-1）/（x+1）
=1/(x+1)+(x-1)²/(x+1)(x-1)×(x+1)/(x-1)
=1/(x+1)+1
=(x+2)/(x+1)
当x=3时
原式=5/4

[1/（x+1）+（x^2-2x+1）/（x^2-1)]/（x-1）/（x+1）
=[1/(x+1)+(x-1)²/(x+1)(x-1)]×(x+1)/(x-1)
=1/(x-1)+1
当x=3时
原式=1/2+1=3/2

Answer 2

你给的题就不明白,用手机把原题拍下来,补充到后面.这题这么简单,唉........检验正确答案你就直接代入,就知道了.式子本身就极为简单.

追问

【1/（x+1）+（x^2-2x+1）/（x^2-1)】/（x-1）/（x+1）

追答

你这样发还是不明白,是1/[(x+1)+(x^2-2X+1)]/(x^2-1)/(x-1)/(x+1)
还是1/(x+1)+[(x^2-2x+1)/(x^2-1)]/(x-1)/(x+1)还是其它情况?要知道,只要有一处看错,答案就会不一样了.所以要求你把原题拍照后上传.

Answer 3

[1/(x+1)+(x^2-2x+1)(x^2-1)]/[(x-1)/(x+1)]
=[1/(x+1)+(x-1)^2/(x-1)(x+1)]/[(x-1)/(x+1)]
=[1/(x+1)+(x-1)/(x+1)]*(x+1)/(x-1)
=1/(x+1)*(x+1)/(x-1)+(x-1)/(x+1)*(x+1)/(x-1)
=1/(x-1)+1
=(1+x-1)/(x-1)
=x/(x-1)
=3/(3-1)
=3/2