[x-1/x²-x-2]÷x²-2x+1/2-x÷[1/x²+x]
=[x-1/(x-2)(x+1)]÷(x-1)^2/2-x*(x+1)x
=(x-1)(2-x)*(x+1)x/(x-2)(x+1)(x-1)^2
=x/1-x
=1/(x-1)-1