Question

Determinati elementele multimi A stiind ca

A={x e Z | (x+4) / (x+1) e Z }



e = apartine

Answer 1

$\frac{x+4}{x+1}$ ∈ Z <=> $\frac{x+1+3}{x+1}$ ∈ Z => ($\frac{x+1}{x+1} + \frac{3}{x+1}$) ∈ Z <=>

<=> $1 + \frac{3}{x+1}$ ∈ Z <=> $\frac{3}{x+1}$ ∈ Z ( caci 1 ∈ Z ) =>

=> x + 1 ∈ $D_{3}$ => x+1 ∈ { -3; -1; 1; 3 } => x ∈ { -4; -2; 0; 2 } => 

=> A = { -4; -2; 0; 2 }