Răspuns:
a)x−13∈Z=>x−1∈D3
D_{3}=\left\{\pm1,\pm3\right\}D3={±1,±3}
1)x - 1 = - 1 = > x = 01)x−1=−1=>x=0
2)x - 1 = 1 = > x = 22)x−1=1=>x=2
3)x - 1 = - 3 = > x = - 23)x−1=−3=>x=−2
4)x - 1 = 3 = > x = 44)x−1=3=>x=4
b) \frac{6}{x + 1} \: \in \: \mathbb{Z} = > x + 1 \: \in \: D_{6}b)x+16∈Z=>x+1∈D6
D_{6}=\left\{\pm1,\pm2,\pm3,\pm6\right\}D6={±1,±2,±3,±6}
1)x + 1 = - 1 = > x = - 21)x+1=−1=>x=−2
2)x + 1 = 1 = > x = 02)x+1=1=>x=0
3)x + 1 = - 2 = > x = - 33)x+1=−2=>x=−3
4)x + 1 = 2 = > x = 14)x+1=2=>x=1
5)x + 1 = - 3 = > x = - 45)x+1=−3=>x=−4
6)x + 1 = 3 = > x = 26)x+1=3=>x=2
7)x + 1 = - 6 = > x = - 77)x+1=−6=>x=−7
8)x + 1 = 6 = > x = 58)x+1=6=>x=5
c) \frac{5}{1 - x} \: \in \: \mathbb{Z} = > 1 - x \: \in \: D_{5}c)1−x5∈Z=>1−x∈D5
D_{5}=\left\{\pm1,\pm5\right\}D5={±1,±5}
1)1 - x = - 11)1−x=−1
- x = - 1 - 1−x=−1−1
- x = - 2 \: | \times ( - 1)−x=−2∣×(−1)
x = 2x=2
2)1 - x = 12)1−x=1
- x = 1 - 1−x=1−1
- x = 0 \: | \times ( - 1)−x=0∣×(−1)
x = 0x=0
3)1 - x = - 53)1−x=−5
- x = - 5 - 1−x=−5−1
- x = - 6 \: | \times ( - 1)−x=−6∣×(−1)
x = 6x=6
4)1 - x = 54)1−x=5
- x = 5 - 1−x=5−1
- x = 4 \: | \times ( - 1)−x=4∣×(−1)
x = - 4x=−4
