Question

Determinati numerele intregi x cu proprietatea ca $\frac{2x+2}{x-2}$ este numar intreg

Answer 1

x-2 |2x+2
x-2|x-2  ⇒x-2|2(x-2)   ⇔x-2|2x-4

x-2|2x+2 -2x+4
x+2 |6  ⇒x+2 ∈{-1,-2,-3,-6,1,2,3,6}

1)x+2=-1  x=-3

2)x+2=-2  x=-4

3)x+2=-3  x=-5

4)x+2=-6  x=-8

5)x+2=1  x=-1

6)x+2=2  x=0

7)x+2=3  x=1

8)x+2=6  x=4