Factorize the following equation by the grouping method
$a^{2} + \frac{1}{a^{2}} - 2 - 3 a + \frac{3}{a}$

(a - \frac{2}{a}) (a - \frac{1}{a} - 1)

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(a - \frac{1}{a}) (a - \frac{1}{3 a} - 1)

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(a - \frac{2}{a}) (a - \frac{1}{a} - 3)

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(a - \frac{1}{a}) (a - \frac{1}{a} - 3)

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Solution

The correct option is D $(a - \frac{1}{a}) (a - \frac{1}{a} - 3)$
$a^{2} + \frac{1}{a^{2}} - 2 - 3 a + \frac{3}{a}$
$= a^{2} + \frac{1}{a^{2}} - 2 \times a \times \frac{1}{a} - 3 a + \frac{1}{a}$
$= {(a - \frac{1}{a})}^{2} - 3 (a - \frac{1}{a})$
$= (a - \frac{1}{a}) (a - \frac{1}{a} - 3)$

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