[tex]a) \frac{3}{x - 1} \: \in \: \mathbb{Z} = > x - 1 \: \in \: D_{3}[/tex]
[tex]D_{3}=\left\{\pm1,\pm3\right\}[/tex]
[tex]1)x - 1 = - 1 = > x = 0[/tex]
[tex]2)x - 1 = 1 = > x = 2[/tex]
[tex]3)x - 1 = - 3 = > x = - 2[/tex]
[tex]4)x - 1 = 3 = > x = 4[/tex]
[tex]b) \frac{6}{x + 1} \: \in \: \mathbb{Z} = > x + 1 \: \in \: D_{6}[/tex]
[tex]D_{6}=\left\{\pm1,\pm2,\pm3,\pm6\right\}[/tex]
[tex]1)x + 1 = - 1 = > x = - 2[/tex]
[tex]2)x + 1 = 1 = > x = 0[/tex]
[tex]3)x + 1 = - 2 = > x = - 3[/tex]
[tex]4)x + 1 = 2 = > x = 1[/tex]
[tex]5)x + 1 = - 3 = > x = - 4[/tex]
[tex]6)x + 1 = 3 = > x = 2[/tex]
[tex]7)x + 1 = - 6 = > x = - 7[/tex]
[tex]8)x + 1 = 6 = > x = 5[/tex]
[tex]c) \frac{5}{1 - x} \: \in \: \mathbb{Z} = > 1 - x \: \in \: D_{5}[/tex]
[tex]D_{5}=\left\{\pm1,\pm5\right\}[/tex]
[tex]1)1 - x = - 1 [/tex]
[tex] - x = - 1 - 1[/tex]
[tex] - x = - 2 \: | \times ( - 1)[/tex]
[tex]x = 2[/tex]
[tex]2)1 - x = 1[/tex]
[tex] - x = 1 - 1[/tex]
[tex] - x = 0 \: | \times ( - 1)[/tex]
[tex]x = 0[/tex]
[tex]3)1 - x = - 5[/tex]
[tex] - x = - 5 - 1[/tex]
[tex] - x = - 6 \: | \times ( - 1)[/tex]
[tex]x = 6[/tex]
[tex]4)1 - x = 5[/tex]
[tex] - x = 5 - 1[/tex]
[tex] - x = 4 \: | \times ( - 1)[/tex]
[tex]x = - 4[/tex]
