Để \(\frac{4x-7}{2x+1}\)nguyên thì
\(4x-7⋮2x+1\)
\(\Rightarrow2\left[2x+1\right]-9⋮2x+1\)
\(\Rightarrow9⋮2x+1\)
=> 2x + 1 \(\inƯ\left[9\right]\in\left\{-9;-3;-1;1;3;9\right\}\)
=> 2x \(\in\left\{-10;-4;-2;0;2;8\right\}\)
=> x \(\in\left\{-5;-2;-1;0;1;4\right\}\)