Question

Enumerati elementele multimii A={x| x ∈ Z \ {-1}, $\frac{3x+2}{x+1}$ ∈ Z}

Answer 1

    
$\frac{3x+2}{x+1} = \frac{2x+x+2}{x+1}=\frac{2x+2+x}{x+1}=\frac{2x+2}{x+1}+\frac{x}{x+1}=\frac{2(x+1)}{x+1}+\frac{x}{x+1}=2+\frac{x}{x+1} \\ \\ \frac{x}{x+1} \;\epsilon \;Z \;\;doar \;daca \;\;x = 0\;sau\;daca\;x=-2 \\ \\ =\ \textgreater \ A = \{ 0;\;-2 \} \\ \\ =\ \textgreater \ \frac{3x+2}{x+1} = \frac{3*0+2}{0+1}= \frac{2}{1}=2 \; \epsilon \; Z\\\frac{3x+2}{x+1} = \frac{3*(-2)+2}{-2+1}= \frac{-4}{-1}=4$