Question

Solve the problem. please​

Answer 1

`\red{\bf A= \{2,4 \}}`

Explanation:

`\bf A = \bigg \{x \in \mathbb{N} \bigg| \: (x + 2)/(x - 1) \in \mathbb{N} \bigg \}`

`\bf x - 1 \: \: \: \bigg| \: \: \: x + 2`

`\bf \underline \: x - 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( - )`

`\bf x - 1 \: \bigg| \: x + 2 - (x - 1)`

`\bf x - 1 \: \bigg| \: x + 2 - x + 1`

`\bf x - 1 \: \big| \:3 \implies x - 1 \in D_(3)`

`\bf x - 1 \in \{1,3 \} \: \: \: \: \bigg| + 1`

`\bf x \in \{2,4 \} \implies \red{\boxed{ \bf A= \{2,4 \}}}`