Question

Determinați valorile întregi ale lui x astfel încât 2 x plus 5 supra x plus 2 să fie număr întreg.​

Answer 1

 

$\displaystyle\bf\\\frac{2x+5}{x+2}=\frac{2x+4+1}{x+2}=\frac{2x+4}{x+2}+\frac{1}{x+2}\\\\\\\frac{2x+4}{x+2}=\frac{2(x+2)}{x+2}=2\in Z\\\\\\\implies~\frac{1}{x+2}\in Z\\\\D_1=\{-1;~1\}\\\\(x+2)\in\{-1;~1\}\\\\x+2=-1\implies x=-1-2 \implies x=-3\\\\x+2=1\implies x=1-2 \implies x=-1\\\\\boxed{\bf x\in \{-3;~-1\}}$