Question

Factorise
$x ^{2} + (1 \div x ^{2}) + 2 - 5x - (5 \div x)$
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Answer 1

$\bf \: Factorize : {x}^{2} + \dfrac{1}{ {x}^{2} } + 2 - 5x - \dfrac{5}{x}$

$\rm :\implies\: \bigg( {x}^{2} + \dfrac{1}{ {x}^{2} } + 2 \bigg) - 5(x + \dfrac{1}{x} )$

$\rm :\implies\: {\bigg (x + \dfrac{1}{x} \bigg)}^{2} - 5(x + \dfrac{1}{x} )$

$\rm :\implies\: \bigg(x + \dfrac{1}{x} \bigg) \bigg(x + \dfrac{1}{x} - 5 \bigg)$