A) \[0\]
B) \[-1\]
C) \[1\]
D) \[2\]
Correct Answer: A
Solution :
\[\frac{1}{1+{{a}^{2}}-a}-\frac{1}{1+{{a}^{2}}+a}-\frac{2a}{1+{{a}^{4}}+{{a}^{2}}}\] \[=\frac{1+{{a}^{2}}-a(1+{{a}^{2}}-a)}{(1+{{a}^{2}}-a)(1+{{a}^{2}}+a)}-\frac{2a}{1+{{a}^{4}}+{{a}^{2}}}\] \[=\frac{1+{{a}^{2}}+a-1-{{a}^{2}}+a}{{{(1+{{a}^{2}})}^{2}}-{{a}^{2}}}-\frac{2a}{1+{{a}^{4}}+{{a}^{2}}}\] \[=\frac{2a}{1+{{a}^{4}}+2{{a}^{2}}-{{a}^{2}}}-\frac{2a}{1+{{a}^{4}}+{{a}^{2}}}\] \[=\frac{2a}{1+{{a}^{4}}+{{a}^{2}}}-\frac{2a}{1+{{a}^{4}}+{{a}^{2}}}=0\]
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