$\frac{4n+1}{2n+3}$
$=>(4n+1)÷(2n+3)<=>(2n+3)÷(2n+3)$
$=>(4n+1)÷(2n+3)<=>2(2n+3)÷(2n+3)$
$=>(4n+1)÷(2n+3)<=>4n+6÷(2n+3)$
$=>(4n+1)-(4n+6)÷(2n+3)$
$=>-5÷(2n+3)<=>(2n+3)∈U(-5)={-1; -5; 1; 5}$
$=>2n={-4; -8; -2; 2}$
$=>n={-2; -4; -1; 1}$
$Xét:$
$+)n=-2$
$=>\frac{4.-2+1}{2.-2+3}=7$
$+)n=-4$
$=>\frac{4.-4+1}{2.-4+3}=3$
$+)n=-1$
$=>\frac{4.-1+1}{2.-1+3}=-3$
$+)n=1$
$=>\frac{4.1+1}{2.1+3}=1$
$=>n=-1$