2$\frac{2n+5}{2n+2}$=$\frac{2n+2+3}{2n+2}$=$\frac{2n+2}{2n+2}$+$\frac{3}{2n+2}$=1+$\frac{3}{3n+2}$
để 2n+5 chia hết cho 2n+2 thì 3 phải chia hết cho 2n+3
$⇒2n+2∈Ư(3)={±1;±3}$
$+)2n+1=1⇔2n=0⇔n=0$
$+)2n+1=-1⇔n=-1$
$+)2n+1=3⇔n=1$
$+)2n+1=-3⇔n=-2$
vậy $n={0;1;1;-1}$
