((a-1)/(a^2-4a+4)-(a+2)/(a^2-2a))÷(4/a-1)
=((a-1)/(a-2)²-(a+2)/a(a-2))÷(4/a-a/a))
=(a(a-1)/a(a-2)²-(a+2)(a-2)/a(a-2)²)÷((4-a)/a)
=(a²-a-a²+4)/a(a-2)²×a/(4-a)
=(-a+4)/a(a-2)²×a/(4-a)
=1/(a-2)²
=1/(2-√3-2)²
=1/3
((a-1)/(a^2-4a+4)-(a+2)/(a^2-2a))÷(4/a-1)
=((a-1)/(a-2)²-(a+2)/a(a-2))÷(4/a-a/a))
=(a(a-1)/a(a-2)²-(a+2)(a-2)/a(a-2)²)÷((4-a)/a)
=(a²-a-a²+4)/a(a-2)²×a/(4-a)
=(-a+4)/a(a-2)²×a/(4-a)
=1/(a-2)²
=1/(2-√3-2)²
=1/3