Question

已知:a=1/根号3,求1-2a+a方/a-1-根号a方-2a+1/a方-a的值

Answer 1

a=1/√3<1
(1-2a+a²)/(a-1)-√(a²-2a+1)/(a²-a)
=(a-1)²/(a-1)-√(a-1)²/a(a-1)
=a-1-(1-a)/a(a-1)
=a-1+a
=2a-1
=2/√3-1
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Answer 2

a=1/√3=√3/(√3*√3)=√3/3<1
1/a=1/(1/√3)=√3

(1-2a+a^2)/(a-1)-√(a^2-2a+1)/(a^2-a)
=(a-1)^2/(a-1)-√(a-1)^2/(a^2-a)
=(a-1)-(1-a)/[a(a-1)]
=(a-1)+(a-1)/[a(a-1)]
=a-1+1/a
=√3/3-1+√3
=2√3/3-1