Question

cine ma ajuta va rog acum dau coronita ex 6.7.9

Answer 1

$\it \dfrac{3x-5}{x-1} \in\ \mathbb{Z} \Rightarrow x-1|3x-5 \ \ \ \ (1)$

$\it x-1|x-1 \Rightarrow x-1|3(x-1) \Rightarrow x-1|3x-3\ \ \ (2)$

Din relațiile (1), (2), rezultă:

$\it x-1|3x-3-(3x-5) \Rightarrow x-1|3x-3-3x+5 \Rightarrow x-1|2\Rightarrow$

$\it \Rightarrow x-1\in D_2 \Rightarrow x-1 \in \{\pm1,\ \pm2\} \Rightarrow x-1 \in\{-2,\ -1,\ 1,\ 2\}|_{+1}$

$\it \Rightarrow x\in\{ -1,\ 0,\ 2,\ 3\}$

Deci, A = {-1, 0, 2, 3} 

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$\it \dfrac{3x-5}{x-1}= \dfrac{3x-3-2}{x-1} =\dfrac{3(x-1)-2}{x-1} = 3-\dfrac{2}{x-1}\in\ \mathbb{Z} \Rightarrow x-1|2$

$\it \Rightarrow x-1\in D_2 \Rightarrow x-1 \in \{\pm1,\ \pm2\} \Rightarrow x-1 \in\{-2,\ -1,\ 1,\ 2\}|_{+1}$

$\it \Rightarrow x\in\{ -1,\ 0,\ 2,\ 3\}$

Deci, A = {-1, 0, 2, 3}