Ta có: $\left \{ {{4x+3 ⋮ 3x+1 } \atop {3x+1 ⋮ 3x+1 }} \right.⇒\left \{ {{3.(4x+3) ⋮ 3x+1} \atop {4.(3x+1) ⋮ 3x+1}} \right.⇒\left \{ {{12x+9 ⋮ 3x+1} \atop {12x+4 ⋮ 3x+1}} \right.$
$⇒(12x+9)-(12x+4) ⋮ 3x+1$
$⇒5 ⋮ 3x+1$
$⇒3x+1∈Ư(5)=${$±1;±5$}
Ta có bảng sau:
$3x+1$ $-1$ $1$ $-5$ $5$
$x$ $-2/3$ $0$ $-2$ $4/3$
Vậy $x∈${$-2/3;0;-2;4/3$}.