Question

Factorize x sq. + 1/(x) sq. -2 -3x + 3/x

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } - 2 - 3x + \frac{3}{x } \\ \\ = {(x - \frac{1}{x}) }^{2} + 2 - 2 - 3(x - \frac{1}{x} ) \\ \\ = {(x - \frac{1}{x} )}^{2} - 3(x - \frac{1}{x} ) \\ \\ = (x - \frac{1}{x} )(x - \frac{1}{x} - 3)$
here,we use the formula,
$\boxed{\boxed{a^2+b^2=(a-b)^2+2ab}}$
$\text{hence, answer is (x - 1/x)(x - 1/x - 3)}$

Answer 2

${x}^{2} + \frac{1}{ {x}^{2} } - 2 - 3x + \frac{3}{x } \\ \\\text{We know,}\\\\a^2+b^2=(a-b)^2+2ab\\\\By \ using \ this,\\\\ = {(x - \frac{1}{x}) }^{2} + 2 - 2 - 3(x - \frac{1}{x} ) \\ \\ = {(x - \frac{1}{x} )}^{2} - 3(x - \frac{1}{x} ) \\ \\ = \boxed{\boxed{(x - \frac{1}{x} )(x - \frac{1}{x} - 3)}}$