a)
[tex]\it \dfrac{2x-1}{x+3}\in \mathbb{Z} \Rightarrow x+3|2x-1 \ \ \ \ (1)
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x+3|x+3 \Rightarrow x+3|(x+3)\cdot2 \Rightarrow x+3|2x+6 \ \ \ \ (2)
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(1), (2) \Rightarrow x+3|2x+6-(2x+1) \Rightarrow x+3|2x+6-2x+1 \Rightarrow
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x+3|7 \Rightarrow x+3\in D_7 \Rightarrow x+3\in\{\pm1,\ \pm7\} \Rightarrow
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\Rightarrow x+3\in\{-7,\ -1,\ 1,\ 7\}|_{-3} \Rightarrow x\in\{-10,\ -4,\ -2,\ 4\} \Rightarrow
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\Rightarrow A = \{-10,\ -4,\ -2,\ 4\}
[/tex]
b)
Probabilitatea se calculează cu formula:
[tex]\it p=\dfrac{nr.\ cazuri\ favorabile}{nr.\ cazuri\ posibile}[/tex]
card(A) = 4 (cazuri posibile)
Avem un singur caz favorabil, elementul 4.
[tex]\it p=\dfrac{1}{4}[/tex]
