a fost răspuns

Determinati elementele multimi A stiind ca

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



e = apartine

Răspuns :

Alexutzuu10ask
[tex] \frac{x+4}{x+1} [/tex] ∈ Z <=> [tex] \frac{x+1+3}{x+1} [/tex] ∈ Z => ([tex] \frac{x+1}{x+1} + \frac{3}{x+1} [/tex]) ∈ Z <=>

<=> [tex]1 + \frac{3}{x+1} [/tex] ∈ Z <=> [tex] \frac{3}{x+1} [/tex] ∈ Z ( caci 1 ∈ Z ) =>

=> x + 1 ∈ [tex] D_{3} [/tex] => x+1 ∈ { -3; -1; 1; 3 } => x ∈ { -4; -2; 0; 2 } => 

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

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