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

问题描述:

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

(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