Question

Determinati numarul natural a pentru care : 2a+7/a+1∈N

Answer 1

 

$\displaystyle\bf\\Se~da:\\\\a\in N\\\\\frac{2a+7}{a+1}\in N\\\\Se~cere:\\\\a=?\\\\Rezolvare:\\\\\frac{2a+7}{a+1}=\frac{2a+2+5}{a+1}=\frac{2a+2}{a+1}+\frac{5}{a+1}=\frac{2(a+1)}{a+1}+\frac{5}{a+1}=2+\frac{5}{a+1}\\\\2\in N\\\\\implies\frac{5}{a+1}\in N\\\\\implies(a+1)\in D_5\\D_5=\{1;~5\}\\\\a+1=1\implies a=0\\a+1=5\implies a=4\\\\\implies~\boxed{\bf a\in \{0;~4\}}$