A) \[\left( x+\frac{1}{x} \right)\left( x+\frac{1}{x}-2 \right)\]
B) \[\left( x-\frac{1}{x} \right)\left( x+\frac{1}{x}-2 \right)\]
C) \[\left( x-\frac{1}{x} \right)\left( x-\frac{1}{x}+2 \right)\]
D) \[\left( x+\frac{1}{x} \right)\left( x-\frac{1}{x}+2 \right)\]
Correct Answer: A
Solution :
(a): \[{{x}^{2}}+\frac{1}{{{x}^{2}}}+2-2x-\frac{2}{x}\] (identify the square term.) \[={{\left( x+\frac{1}{x} \right)}^{2}}-2\left( x+\frac{1}{x} \right)\] \[=\left[ x+\frac{1}{x} \right]\left[ x+\frac{1}{x}-2 \right]\]
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