Question

Determinați mulțimea A={x aparține Z | 3x-5/2x+1 aparține Z}

Answer 1

$\displaystyle \dfrac{3x-5}{2x+1}\in Z\implies 2x+1|3x-5 \\ \\ 2x+1|6x-10 \\ \\ 2x+1|3(2x+1)-13 \\ \\ 2x+1|-13 \\ \\ 2x+1\in D_{-13} \\ \\ 2x+1\in\{\pm 1 \ ; \ \pm 13\}|-1 \\ \\ 2x\in\{ 0;-2;-14;12\} |:2 \\ \\ x\in\{ 0;-1;-7;6\} \\ \\ A=\{ 0;-1;-7;6\}$