(x^2-4/x^2-4x+4)÷(x+2/x+1)-x/x-2
=(x+2)/(x-2)(x+2) *(x+1)/(x+2)-x/x-2
=(x+1)/(x-2)(x+2)-x(x+2)/(x-2)(x+2)
=(-x^2-2x+x+1)/(x-2)(x+2)
=(-x^2-x+1)/(x^2-4)
(x^2-4/x^2-4x+4)÷(x+2/x+1)-x/x-2
=(x+2)/(x-2)(x+2) *(x+1)/(x+2)-x/x-2
=(x+1)/(x-2)(x+2)-x(x+2)/(x-2)(x+2)
=(-x^2-2x+x+1)/(x-2)(x+2)
=(-x^2-x+1)/(x^2-4)