2x^3(x^2+2x)^-1/2 -(x^2+2x)^1/2 / x^2
the whole numerator is over x^2
common factor is (x^2 + 2x)^(-1/2) so
(x^2 + 2x)^(-1/2)[2x^3 - x^2 - 2x]/x^2
= x(x^-1/2)(x+2)^(-1/2)[x^2 - x - 2]/x^2
= x^(-1/2)(x+2)^(-1/2)(x-2)(x+1)/x
= (x-2)(x+1)/[x^(3/2)(x+2)^(1/2)]