已知a=根号5-根号3,求(2+1/a-1-1/a+1)÷(a+a/a²-1)的值

问题描述:

已知a=根号5-根号3,求(2+1/a-1-1/a+1)÷(a+a/a²-1)的值

[2+1/﹙a-1﹚-1/﹙a+1﹚]÷[a+a/﹙a²-1﹚]
=﹙2a²-2+a+1-a+1﹚÷﹙a³-a+a﹚
=2a²/a³
=2/a
=2/﹙√5-√3﹚
=2﹙√5+√3﹚/[﹙√5-√3﹚﹙√5+√3﹚]
=2﹙√5+√3﹚/2
=√5+√3