why what how理论:这两题怎么做?(初中数学)

来源:百度文库 编辑:高考问答 时间:2024/04/26 12:11:47
这题有什么简便方法做?难道只有通分做?
是分式

(x^3+2)/(x^2-x+1) + (x^3-2)/(x^2+x+1) - 2x
不求答案,只求一方法

若分式方程

(k-1)/(x^2-1) - 1/(x^2-x) = (k-5)/x^2+x

有增根x= -1 则K的值是 ( )

A . 1 B. 3 C. 6 D.9

步骤稍微详细些

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

2]两边通分后将x=-1求解,选D