已知x=2+2的算术平方根,求代数式（x^2+2x+1）/（x^2-1）-x/(x-1）的值_数学解答

已知x=2+2的算术平方根,求代数式（x^2+2x+1）/（x^2-1）-x/(x-1）的值

人气：408 ℃　时间：2020-04-05 23:33:25

解答

（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)
=1/(2+√2-1)
=1/(√2+1)
=√2-1