A) \[\left( x-\frac{1}{a} \right)\] and \[(x+a)\]
B) \[\left( x-\frac{1}{{{a}^{2}}} \right)\] and \[(x+a)\]
C) \[\left( x-\frac{1}{{{a}^{2}}} \right)\] and \[(x-a)\]
D) \[\left( x+\frac{1}{{{a}^{2}}} \right)\] and \[(x+a)\]
Correct Answer: A
Solution :
\[{{x}^{2}}+\frac{{{a}^{2}}-1}{a}x-1={{x}^{2}}+\left( \frac{{{a}^{2}}}{a}-\frac{1}{a} \right)x-1\] \[={{x}^{2}}+ax-\frac{x}{a}-1\] \[=\left( {{x}^{2}}-\frac{x}{a} \right)+(ax-1)\] \[=x\left( x-\frac{1}{a} \right)+a\left( x-\frac{1}{a} \right)\] \[=\left( x-\frac{1}{a} \right)\,(x+a)\]
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