My differentiation problem is:

$\displaystyle y=(\frac{1}{x} - x)^3$

I get to:

$\displaystyle \frac{dy}{dx} = 3(x^{-1} - x)^2 . -x^{1/2} $

= $\displaystyle \frac{-3}{x^2} (x^{-1} - x)^2 $

But book answer says:

$\displaystyle 3(\frac{1}{x} + x)^2 (1 - \frac{1}{x^2})$

How do they get to that?