Question

Factorise $x^2+\frac{1}{x^2}+2-3x-\frac{3}{x}.$

Answer 1

We have,

$x^2+\frac{1}{x^2}+2-3x-\frac{3}{x}$

$\Rightarrow (x+\frac{1}{x}{)}^2-3(x+\frac{1}{x})$

$\Rightarrow (x+\frac{1}{x}-3)(x+\frac{1}{x})$

Hence, this is the answer.