A) \[\frac{16{{x}^{4}}+9{{x}^{2}}+1}{4{{x}^{3}}+x}\]
B) \[\frac{16{{x}^{4}}+8{{x}^{2}}+2}{4{{x}^{3}}+x}\]
C) \[\frac{4{{x}^{3}}+x}{16{{x}^{4}}+8{{x}^{2}}+9}\]
D) None of these
Correct Answer: A
Solution :
\[A+\frac{1}{A}=\frac{4{{x}^{2}}+1}{x}+\frac{x}{(4{{x}^{2}}+1)}\] \[=\frac{{{(4{{x}^{2}}+1)}^{2}}+{{x}^{2}}}{x(4{{x}^{2}}+1)}\] \[=\frac{16{{x}^{4}}+9{{x}^{2}}+1}{4{{x}^{2}}+x}\]
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