[tex] \dfrac{18}{2x+1} \in N \iff 2x+1 \in D_{18} \\ \\ D_{18} = \{ 1, 2, 3, 6, 9, 18\} \\ \\ 2x+1 = 1 \Rightarrow 2x=0 \Rightarrow x=0 \in N \\ \\ 2x+1 = 2 \Rightarrow 2x = 1 \Rightarrow x = \dfrac{1}{2} \notin N \\ \\ 2x+1 = 3 \Rightarrow 2x = 2\Rightarrow x=1 \in N \\ \\ 2x+1 = 6 \Rightarrow 2x = 5 \Rightarrow x = \dfrac{5}{2} \notin N \\ \\ 2x+1 = 9 \Rightarrow 2x = 8 \Rightarrow x = 4 \in N \\ \\ 2x+1 = 18 \Rightarrow 2x = 17 \Rightarrow x = \dfrac{17}{2} \notin N \\ \\ \\ x \in \{0, 1, 4 \}[/tex]
