Chọn: Đáp án B

$\frac{2x+1}{x+2}=-x+m\Rightarrow 2x+1={{x}^{2}}+mx-2x+2m-2x+2m\Rightarrow {{x}^{2}}+\left( 4-m \right)x+1-2m=0$

$k=1,a=1,b=\left( 4-m \right),c=1-2m$

$A{{B}^{2}}=\frac{{{k}^{2}}+1}{{{a}^{2}}}\left( {{b}^{2}}-4ac \right)=\frac{2}{1}\left( {{\left( 4-m \right)}^{2}}-4\left( 1-2m \right) \right)=2\left( {{m}^{2}}+12 \right)=30\Rightarrow {{m}^{2}}=3\Rightarrow m=\pm \sqrt{3}$