$\frac{A}{B}$ as the sum of distinct inverse naturals.

Question

Is there a method to taking some rational number and expressing it as the sum of distinct inverses of the natural numbers? For example, $$\frac{2}{3} = \frac{1}{6} + \frac{1}{2}$$ and $$\frac{47}{60} = \frac{1}{3} + \frac{1}{4} + \frac{1}{5}$$. If there is some way to go in reverse, does it work for every rational number, and is it the only way?