Question

factorise x²+1/x²+3-2x-2/x​

Answer 1

$x ^{2} + \frac{1}{2} + 2 - 2x - \frac{2}{x}$

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

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

$=(x + \frac{1}{x})( x + \frac{1}{x} ) - 2(x + \frac{1}{x} )$

$=(x + \frac{1}{x} ) (x + \frac{1}{x } - 2)$

$hence, x^{2} + \frac{1}{2} + 2 - 2x - \frac{2}{x} =(1x + \frac{1}{x}) (x + \frac{1}{x} - 2)$