Question

factorise
x*2+1/x*2+3-2x-2/x

Answer 1

Answer:

x²+1/x² +2 -2x-2/x

=(x+1/x)² - 2(x+1/x)

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

Answer 2

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

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

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

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

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

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