Question

a) Aflati x ∈ Z ,x=? a.i.. 5x+7/2x+1 ∈ Z
/=supra
b)x-1/3x-1 ∈ N tot asa /=supra

Answer 1

2x+1|5x+7 |.2
2x+1|2x+1 |.5
2x+1|10x+14
2x+1|10x+5
2x+1| 10x+14-(10x+5)
2x+1|9
$2x+1 \in\{-9,-3,-1,1,3,9\} |-1 \\ 2x\in\{-10,-4,-2,0,2,8\} |:2 \\ x\in\{-5,-2,-1,0,1,4\}$
b) 3x-1|x-1 |.3
3x-1|3x-1
3x-1|3x-3
3x-1|3x-1
3x-1|3x-1-(3x-3)
3x-1|2
$3x-1\in \{-2,-1,1,2\} \\ 3x\in \{-1,0,2,3\} \\ x\in \{0,1\}$