(x+1)/x ÷ [x-(1+x^2)/2x]
=(x+1)/x ÷ [(2x^2-1-x^2)/2x]
=(x+1)/x ÷ [(x^2-1)/2x]
=(x+1)/x × [2x/(x+1)(x-1)]
=2/(x-1)
当 x=√2+1时
原式 = 2/(√2+1)
= 2(√2-1)