This is a very interesting word problem that I came across in an old textbook of mine. So I managed to make a formula redefining the question, but other than that, the textbook gave no hints really and I'm really not sure about how to approach it. Any guidance hints or help would be truly greatly appreciated. Thanks in advance :) So anyway, here the problem goes:
Find two fractions so that their sum added to their product equals $1$.
In other words:
Given integers $a$ and $b$ with $\frac ab < 1,$ find integers $c$ and $d$ such that $\frac ab + \frac cd + \frac ab \cdot\frac cd = 1$