Bài giải:

$\text{K=}\left( \frac{\text{a}}{\text{a-1}}-\frac{1}{{{a}^{2}}-a} \right)\text{: }\left( \frac{\text{1}}{\text{a}+\text{1}}+\frac{2}{{{a}^{2}}-1} \right)$

 $\text{K=}\left( \frac{\text{a}}{\text{a-1}}-\frac{1}{a(a-1)} \right)\text{: }\left( \frac{\text{1}}{\text{a}+\text{1}}+\frac{2}{(a-1)(a+1)} \right)$

K = $\frac{{{a}^{2}}-1}{a(a-1)}:\frac{a-1+2}{(a-1)(a+1)}$

K = $\frac{a+1}{a}:\frac{a+1}{(a-1)(a+1)}$

K = $\frac{a+1}{a}.(a-1)$

K = $\frac{{{a}^{2}}-1}{a}=a-\frac{1}{a}$

Vậy kết quả là: A.