Question

Determina multimea A= { x ∈ Z | $\frac{3x-5}{x-1}$∈ Z }

Va rogg !!

Answer 1

$\frac{3x-5}{x-1}$  ∈ Z
⇒          x-1| 3x-5
 stim ca x-1|x-1   /*(-3)
             x-1|3x-5
             x-1|-3x+3       +
---------------------------------
             x-1|-2 rezulta x-1 ∈ D-2={-2,-1,1,2}
    x-1=-2     x=-1
    x-1=-1     x=0
    x-1=1      x=2
    x-1=2      x=3
deci A={-1,0,2,3}