I was trying to follow a math forum thread when suddenly I stumbled upon a transformation that I just couldn't understand. It goes as follows:
$$v = \sqrt{ \frac{2 U}{r} - \frac{2 U}{r_0}} \implies v = \frac{dr}{dt} = \sqrt{ \frac{2 U r_0 - 2 U r } {rr_0}}$$
Can anyone please explain me how we got from the fist statement to the second? What sort of rules are employed here?
HINT: Forget about the square root. Do you know how to calculate $\frac12+\frac13$?