Question

分子分母同除根号x，第二步里分母里的第二个根号怎么求的呀

Answer 1

利用
(a-b)(a+b)= a^2-b^2
a=√[x+√(x+√x)] , b=√x
//
√[x+√(x+√x)] -√x
=[√[x+√(x+√x)] -√x].[√[x+√(x+√x)] +√x]/[√[x+√(x+√x)] +√x]
=[ [x+√(x+√x)] -x] /[√[x+√(x+√x)] +√x]
=√(x+√x) /[√[x+√(x+√x)] +√x]