先化简,再求值:a²-1/a²-2a+1÷a+1/a³-a²,其中a=根号3

来源：学生作业学帮网编辑：学帮网时间：2024/07/06 19:47:57

a²-1/a²-2a+1÷a+1/a³-a²
=（a+1）(a-1)/(a-1)²÷(a+1)/a²(a-1)
=a²
=(√3)²
=3

（a²-1）/(a²-2a+1)÷（a+1）/(a³-a²)
=（a+1)/(a-1)*a^2(a-1)/(a+1)
=a^2
当a=√3 时，
a^2=3

[（a²-1）/（a²-2a+1）]÷[﹙a+1﹚/﹙a³-a²﹚]
=[（a-1）（a+1）/﹙a-1﹚²][a²﹙a-1﹚/﹙a+1﹚]
=a²
当a=√3 则a²=3