Question

先化简再求值（1-1/a+1）-a/a平方+2a+1其中a=根号3-1

Answer 1

(1-1/(a+1)) -a/(a^2+2a+1)

= ((a+1-1)/(a+1)) -a/(a+1)^2

= a/(a+1)-a/(a+1)^2

= (a^2+a-a)/(a+1)^2

= a^2/(a+1)^2

由 a=√3-1,得

原式 = (√3-1)^2/ (√3-1+1)^2

= (3-2√3+1)/3

= (4-2√3)/3