当x=根号2+1时,求(x-3/x^2-1)/(x-3/(x+1)^2)-(1/x-1)

题目

当x=根号2+1时,求(x-3/x^2-1)/(x-3/(x+1)^2)-(1/x-1)

答案

原式=(x-3)/(x+1)(x-1)*(x+1)²/(x-3)-1/(x-1)
=(x+1)/(x-1)-1/(x-1)
=x/(x-1)
=(√2+1)/(√2-1-1)
=(√2+1)/√2
=(2+√2)/2