Chọn: Đáp án A

$\left( \frac{{{a}^{0,5}}+2}{a+2{{a}^{0,5}}+1}-\frac{{{a}^{0,5}}-2}{a-1} \right).\frac{{{a}^{0,5}}+1}{{{a}^{0,5}}}=\frac{1}{{{a}^{0,5}}}\left[ \frac{{{a}^{0,5}}+2}{{{a}^{0,5}}+1}-\frac{\left( {{a}^{0,5}}-2 \right)\left( {{a}^{0,5}}+1 \right)}{a-1} \right]$

$=\frac{1}{{{a}^{0,5}}}\left( \frac{a+{{a}^{0,5}}22}{a-1}-\frac{a-{{a}^{0,5}}-2}{a-1} \right)=\frac{1}{{{a}^{0,5}}}.\frac{2{{a}^{0,5}}}{a-1}=\frac{2}{a-1}$