[tex]\dfrac{6}{x-1}\in\mathbb{N}\ \text{if (x-1) is a divisor of 6}\\\\\text{divisors of 6:}\ \{1,\ 2,\ 3,\ 6\}\\\\x-1=1\ \ \ |+1\\\boxed{x=2}\in\mathbb{N}\\\\x-1=2\ \ \ \ |+1\\\boxed{x=3}\in\mathbb{N}\\\\x-1=3\ \ \ \ |+1\\\boxed{x=4}\in\mathbb{N}\\\\x-1=6\ \ \ \ \ |+1\\\boxed{x=7}\in\mathbb{N}\\\\Answer:\ A=\{2,\ 3,\ 4,\ 7\}[/tex]
