Question

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

Answer 1

We have,

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

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

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

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

Hence, this is the answer.