已知x=1+根号2,求代数式(x^2+2x+1)/(x^2-1)—x/(x-1)的值

问题描述:

已知x=1+根号2,求代数式(x^2+2x+1)/(x^2-1)—x/(x-1)的值

(x^2+2x+1)/(x^2-1)—x/(x-1)
=(x+1)²/(x+1)(x-1)-x/(x-1)
=(x+1)/(x-1)-x/(x-1)
=1/(x-1)
当x=1+√2时
原式=1/(1+√2-1)
=√2/2