[tex]\displaystyle\\
d)\\
\frac{9n+14}{3n+1} =\frac{9n+3+11}{3n+1}=\\\\
=\frac{9n+3}{3n+1}+\frac{11}{3n+1}=\frac{3(3n+1)}{3n+1}+\frac{11}{3n+1}=3+\frac{11}{3n+1}\\\\
\frac{11}{3n+1}\in Z \Longrightarrow 11~\vdots~(3n+1)\Longrightarrow (3n+1)\in D_{11}
[/tex]
[tex]\displaystyle\\
D_{11Z}=\{-11;-1;1;11\}\\\\
3n+1=-11\Rightarrow 3n=-11-1\Rightarrow 3n=-12\Rightarrow n=\frac{-12}{3}=\boxed{-4}\\
3n+1=-1\Longrightarrow 3n=-1-1\Longrightarrow 3n=-2\Longrightarrow n= \frac{-2}{3}\notin Z \\
3n+1=1\Longrightarrow 3n=1-1\Longrightarrow 3n=0 \Longrightarrow n= \frac{0}{3}=\boxed{0}\\
3n+1=11\Longrightarrow 3n=11-1\Longrightarrow 3n=10 \Longrightarrow n= \frac{10}{3} \notin Z\\
n \in \{-4;0\}[/tex]
