A) \[0\]
B) \[{{x}^{m}}\]
C) \[1\]
D) \[{{x}^{-m}}\]
Correct Answer: C
Solution :
\[\frac{1}{1+\frac{1}{{{x}^{m}}}}+\frac{1}{1+{{x}^{m}}}\] (Since \[{{a}^{-m}}=\frac{1}{{{a}^{n}}}\]) \[=\frac{1}{\frac{{{x}^{m}}+1}{{{x}^{m}}}}+\frac{1}{1+{{x}^{m}}}\] \[=\frac{{{x}^{m}}}{{{x}^{m}}+1}+\frac{1}{{{x}^{m}}+1}\] \[=\frac{{{x}^{m}}+1}{{{x}^{m}}+1}=1\]
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