Question

Factorise:-x²+1/x²+2-2x-2/x

Answer 1

$<b>Heya mate. (^_-). Solution below.$
====================================

x² - (1/x²) + 2 - 2x - (2/x)


• We factorise this polynomial using the method of taking out the common factor.


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

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

• Using the identity : a² + 2ab + b² = (a + b)²


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

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

$<marquee>Hence, the answer is [x + (1/x)] [x + (1/x) - 2].</marquee>$
====================================

Thank you.. ;-)