先化简再求值:1/(a-1)+ a²-4a+4/a²-1·a+1/a-2 其中a=√2+1
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 11:56:27
![先化简再求值:1/(a-1)+ a²-4a+4/a²-1·a+1/a-2 其中a=√2+1](/uploads/image/z/1106800-16-0.jpg?t=%E5%85%88%E5%8C%96%E7%AE%80%E5%86%8D%E6%B1%82%E5%80%BC%EF%BC%9A1%2F%28a-1%29%2B+a%26%23178%3B-4a%2B4%2Fa%26%23178%3B-1%C2%B7a%2B1%2Fa-2+%E5%85%B6%E4%B8%ADa%3D%E2%88%9A2%2B1)
先化简再求值:1/(a-1)+ a²-4a+4/a²-1·a+1/a-2 其中a=√2+1
先化简再求值:1/(a-1)+ a²-4a+4/a²-1·a+1/a-2 其中a=√2+1
先化简再求值:1/(a-1)+ a²-4a+4/a²-1·a+1/a-2 其中a=√2+1
原式=1/(a-1)+ (a-2)²/(a-1)×(a+1)× a+1/a-2
(到这一步,(a-2)²和a-2化简成a-2,(a-1)×(a+1)和 a+1化简成a-1)
=1/(a-1)+ a-2/a-1
(合并同类项)
=(1+ a-2)/a-1
=1
∴无论a为何值,原式值都为1