Factorise:

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

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

$=\left[x^{2}+\left(\frac{1}{x}\right)^{2}-2 \times x \times \frac{1}{x}\right]-1$

$=\left(x-\frac{1}{x}\right)^{2}-1^{2} \quad\left[a^{2}-2 a b+b^{2}=(a-b)^{2}\right]$

$=\left(x-\frac{1}{x}+1\right)\left(x-\frac{1}{x}-1\right) \quad\left[a^{2}-b^{2}=(a-b)(a+b)\right]$