Question

One of the factors of
$x^2+\frac{1}{x^2}+2-2x-\frac{2}{x}$ is

• A. $x-\frac{1}{x}$
• B. $x+\frac{1}{x}-1$
• C. $x+\frac{1}{x}$
• D. $x^2+\frac{1}{x^2}$

Answer 1

The correct option is C $x+\frac{1}{x}$

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

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

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

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