作业帮关于分式的题（x-1)[1-(x+1)/(x-1/x)]
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/08 20:24:36
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关于分式的题（x-1)[1-(x+1)/(x-1/x)]
关于分式的题
（x-1)[1-(x+1)/(x-1/x)]
关于分式的题（x-1)[1-(x+1)/(x-1/x)]
（X-1）[1-(X+1)/(X-1/X)]
= （X-1）[ 1- (X+1) (X/(X²-1)]
= （X-1）[1-(X²+X)/(X²-1)]
= （X-1）｛(X²-1-X²-X)/(X²-1)
= （X-1）｛(-X-1)/[(X+1)(X-1)]｝
= (-(X+1) ｛(X-1))/[(X+1)(X-1)]｝
= -1
如果写在作业本或者试卷上,就不用写大括号的了；我是因为这里写分数线写不了,才加了个大括号上去,方便看
（x-1)[1-(x+1)/(x-1/x)]
=（x-1)[1-(x+1)/(x+1)(x-1)/x]
=（x-1)[1-(x+1)*x/(x+1)(x-1)]
=（x-1)[1-x/x-1]
=（x-1)*1-(x-1)*(x/x-1)
=(x-1)-x
=-1
原式=（x-1)[1-(x+1)*(x/x-1)]
=（x-1)[1-(x+1)x/（x-1)]
=（x-1)-(x+1)x 【把（x-1)乘进去中括号的每一项
=x-1-x²-x
=-x²-1
（x-1)[1-(x+1)/(x-1/x)]
=（x-1)[1-(x+1)/(x+1)(x-1)/x]
=（x-1)[1-(x+1)*x/(x+1)(x-1)]
=（x-1)[1-x/x-1]
=（x-1)*1-(x-1)*(x/x-1)
=(x-1)-x
=-1
这个够不够详细？
（x-1)[1-(x+1)/(x-1/x)]
=(x-1)[(x-1/x-x-1)/(x-1/x)]
=(x-1)[(-1/x-1)/(x-1/x)]
=(x-1)[(-x-1)/(x^2-1)]
=-(x^2-1)/(x^2-1)
=-1