Question

factorize x2+1/x2-2-3x+3/x

Answer 1

Seems your question is ----> x² + 1/x² - 2 - 3x + 3/x

So, x² + 1/x² - 2 - 3x + 3/x
= (x - 1/x)² + 2x.1/x - 2 - 3(x - 1/x)
Note :- a² + b² = (a - b)² + 2ab , here in place of a use x and in place of b use 1/x then, x² + 1/x² = (x - 1/x)² + 2x.1/x ]

= (x - 1/x)² + 2 - 2 -3(x - 1/x)
= (x - 1/x)² - 3(x - 1/x)
= (x - 1/x)(x - 1/x - 3)

Hence, factorization of given polynomial is (x - 1/x)(x - 1/x - 3)

Answer 2

${x}^{2} + \frac{1}{ {x}^{2} } - 2 - 3x + \frac{1}{3x} \\ \\ \\ = {x}^{2} + \frac{1}{ {x}^{2} } - 2(x \times \frac{1}{x} ) - 3(x - \frac{1}{x} ) \\ \\ \\ => {(x - \frac{1}{x}) }^{2} - 3(x - \frac{1}{x} ) \\ \\ \\ = > (x - \frac{1}{x} )(x - \frac{1}{x} - 3)$