原式=(1-2a+a²)/(a-1) -√(a²-2a+1)/(a²-a) -a
=(a-1)²/(a-1) -√(a-1)²/ [a(a-1)] -a
=a-1 -|a-1|/[a(a-1)] -a
∵ a=2-√3
∴ a-1=1-√3﹤0
原式=a-1 +(a-1)/[a(a-1)] -a
=a-1 +1/a -a
=-1 + 1/a
=-1 + 1/(2-√3)
=-1 +(2+√3)/[(2+√3)(2-√3)]
=-1 +(2+√3)/(4-3)
=-1+2+√3
=1+√3