9. Suppose the fraction $\frac{n-13}{5 n+6}(n \neq 13)$ is not in its simplest form. Then, the smallest positive integer value of $n$ can be ( ).
(A) 84
(B) 68
(C) 45
(D) 115
9.A.

Let $d$ be a common divisor of $n-13$ and $5 n+6$, then
$$
\begin{array}{l}
d|(n-13), d|(5 n+6) \\
\Rightarrow d|[(5 n+6)-5(n-13)] \Rightarrow d| 71 .
\end{array}
$$

Since 71 is a prime number, then $d=71$.
As $d \mid(n-13)$, so, $n-13 \geqslant 71$.
Hence $n \geqslant 84$.