Question

先化简再求值 （2a/a-1 + a/1-a ）/a 其中a=根号2 +1

求详细过程

Answer 1

解
[2a/(a-1)+a/(1-a)]/a
=[2a/(a-1)-a/(a-1)]/a
=(2a-a)/(a-1)/a
=a(a-1)÷a
=a-1
=√2+1-1
=√2

追问

你的第三步和第四步有没有问题

追答

=[(2a-a)/(a-1)]/a
=[a/(a-1)]÷a
=1/(a-1)
=1/(√2+1-1)
=1/√2
=√2/2

Answer 2

(2a/(a-1)+a/(1-a))/a=(2a/(a-1)-a/(a-1))/a=(a/(a-1))/a=1/(a-1) 带入值=1/(根号2+1-1)=1/根号2=根号2/2