Question

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

先化简，再求值 其中a=根号3

Answer 1

原式=(a²+a+1/4)-(a²-a+1/4)+1/(a+1)+1/(a-1)
=a²+a+1/4-a²+a-1/4+[(a-1+a+1)/[(a+1)(a-1)]
=2a+(2a)/(a²-1)
=2√3+2√3/(3-1)
=2√3+√3
=3√3

Answer 2

=(a+1/2+a-1/2)(a+1/2-a+1/2)
+(a-1-a-1)(a-1)(a+1)
=2a-2/(a^2-1)
=2根号3-2/(3-1)
=2根号3-1

Answer 3

解：
(a^2+1)/(a-1)-a+1
=(a^2+1)/(a-1)-(a-1)
=（a^2+1）/(a-1)-(a-1)^2/(a-1)
=[（a^2+1）-(a-1)^2]/(a-1)
=(a^2+1-a^2+2a-1)/(a-1)
=2a/(a-1)