Question 10
Write $\frac{21}{22} = \frac{a}{b} + \frac{c}{d}$ with nonzero natural $a , b , c , d$; $\frac{a}{b} , \frac{c}{d} , \frac{b}{d}$ all reduced. How many decompositions are there, ignoring order? For example $\frac{1}{2} + \frac{5}{11}$ and $\frac{5}{11} + \frac{1}{2}$ count as one.