(a/b)' = (a'b - ab')/b^2
f(x)'
= {(x-2)'[x(x+1)] - (x-2)[x(x+1)]'}/[x^2(x+1)^2]
= {x(x+1) - (x-2)(2x+1)}/[x^2(x+1)^2]
= {x^2 + x - 2x^2 + 3x +2}/[x^2(x+1)^2]
= (-x^2 + 4x + 2) /[x^2(x+1)^2]