AMC 10 2021-fall-b Problem 7

Call a fraction $\frac{a}{b}$, not necessarily in the simplest form, special if $a$ and $b$ are positive integers whose sum is $15$. How many distinct integers can be written as the sum of two, not necessarily different, special fractions? $\textbf{(A)}\ 9 \textbf{(B)}\ 10 \textbf{(C)}\ 11 \textbf{(D)}\ 12 \textbf{(E)}\ 13$