Show that $d \geq b+f$. Let $a, b, c, d, e, f$ be positive integers such that:
$$\dfrac{a}{b}<\dfrac{c}{d}<\dfrac{e}{f}$$
Suppose $af - be = -1$. Show that $d \geq b+f$.
Looked quite simple at first sight...but havent been able to solve this inequality. Have no idea where to start. Need help. Thanks!!

Hint: Try to derive that $bf<d$. What can you conclude from there?
(Hint 2: $bf = (b-1)(f-1) + (b+f) - 1$.)
