Bài giải:

$\frac{({{x}^{2}}-y)(y+1)+{{x}^{2}}{{y}^{2}}-1}{({{x}^{2}}+y)(y+1)+{{x}^{2}}{{y}^{2}}+1}$= $\frac{{{x}^{2}}y-{{y}^{2}}+{{x}^{2}}-y+{{x}^{2}}{{y}^{2}}-1}{{{x}^{2}}y+{{y}^{2}}+{{x}^{2}}+y+{{x}^{2}}{{y}^{2}}+1}$

= $\frac{({{x}^{2}}y-y)+({{x}^{2}}{{y}^{2}}-{{y}^{2}})+({{x}^{2}}-1)}{({{x}^{2}}y+y)+({{x}^{2}}{{y}^{2}}+{{y}^{2}})+({{x}^{2}}+1)}$ = $\frac{y({{x}^{2}}-1)+{{y}^{2}}({{x}^{2}}-1)+({{x}^{2}}-1)}{y({{x}^{2}}+1)+{{y}^{2}}({{x}^{2}}+1)+({{x}^{2}}+1)}$

= $\frac{(y+{{y}^{2}}+1)({{x}^{2}}-1)}{(y+{{y}^{2}}+1)({{x}^{2}}+1)}$ = $\frac{{{x}^{2}}-1}{{{x}^{2}}+1}$

Vậy đáp án đúng là: C