Question

factorise x square+1/x square+2-2x-2/x

Answer 1

Hope u like my process
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$= > {x}^{2} + \frac{1}{ {x}^{2} } + 2 - 2x - \frac{2}{x} \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2x. \frac{1}{x} - 2(x + \frac{1}{x} ) \\ \\ = > {(x + \frac{1}{x} )}^{2} - 2(x + \frac{1}{x} ) \\ \\ = > (x + \frac{1}{x} )(x + \frac{1}{x} - 2) \\ \\ \mathcal{the \: \: required \: \: factorization \: \: is} \\ \\ = > \underline{(x + \frac{1}{x} )(x + \frac{1}{x} - 2) }$
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Hope this is ur required answer

Proud to help you

Answer 2

$<b > Ello!!$

Here's your answer

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To factorise : x² + 1 / x² + 2 - 2x - 2 / x

Now ,

x² + 1 / x² + 2 - 2x - 2 / x

= { ( x )² + ( 1 / x )² + 2 . x . 1 / x } - 2x + 2 / x [ • ( x . 1 / x ) = 1 ]

= ( x + 1 / x )² - 2 ( x + 1 / x )

[ • ( a + b )² = a² + b² + 2ab → Using this identity ]

= ( x + 1 / x ) ( x + 1 / x - 2 ) [ ★ Required answer ]

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Hope it helps!!

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