先化简,在求值:(a²+2a+1)/(a²-1) - a/(a-1) 其中a√3+1

分类: 作业答案 • 2023-01-07 18:03:08

问题描述：

先化简,在求值:(a²+2a+1)/(a&sup2-1) - a/(a-1) 其中a√3+1

答

:(a²+2a+1)/(a²-1) - a/(a-1)
=(a+1)²/[(a+1)(a-1)]-a/(a-1)
=(a+1)/(a-1)-a/(a-1)
=(a+1-a)/(a-1)
=1/(a-1)
当a=√3+1时
原式= 1/(√3+1-1)
=1/√3
=√3/3