A) \[\frac{4{{x}^{4}}+8{{x}^{2}}+4}{{{x}^{2}}-2x-1}\]
B) \[\frac{4{{x}^{4}}+8{{x}^{2}}+4}{{{x}^{4}}-2{{x}^{2}}-1}\]
C) \[\frac{4{{x}^{4}}+8{{x}^{2}}+4}{{{x}^{4}}-2{{x}^{2}}+1}\]
D) None of the above
Correct Answer: C
Solution :
\[{{(A+B)}^{2}}={{\left[ \left( \frac{x-1}{x+1} \right)+\left( \frac{x+1}{x-1} \right) \right]}^{2}}\] \[={{\left[ \frac{{{(x-1)}^{2}}+{{(x+1)}^{2}}}{(x+1)(x-1)} \right]}^{2}}\] \[={{\left[ \frac{2({{x}^{2}}+1)}{{{x}^{2}}-1} \right]}^{2}}=\frac{4({{x}^{4}}+2{{x}^{2}}+1)}{{{x}^{4}}-2{{x}^{2}}+1}\] \[=\frac{4{{x}^{4}}+8{{x}^{2}}+4}{{{x}^{4}}-2{{x}^{2}}+1}\]
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