Question

Fie 2x+3/x-1 apartine Z, x diferit de 1.Aflati valorile lui x.

Answer 1

(2x+3)/(x-1)∈Z

(2x-2+5)/(x-1)∈Z
(2x-2)/(x-1)+5/(x-1)∈Z
2(x-1)/(x-1)+5/(x-1)∈Z

2+5/(x-1)∈Z
dar 2∈Z⇒5/(x-1)∈Z⇒x-1∈DZ5
x-1=1......... x=2
x-1=5.........x=6
x-1=-1........x=0
x-1=-5........x=-4
S={-4;0;2;6}care verifica toate si toate∈Z\{1}