Question:
Factorize:
$x^{2}+\frac{1}{x^{2}}-2-3 x+\frac{3}{x}$
Solution:
We have :
$x^{2}+\frac{1}{x^{2}}-2-3 x+\frac{3}{x}$
$=x^{2}-2+\frac{1}{x^{2}}-3 x+\frac{3}{x}$
$=(x)^{2}-2 \times x \times \frac{1}{x}+\left(\frac{1}{x}\right)^{2}-3\left(x-\frac{1}{x}\right)$
$=\left(x-\frac{1}{x}\right)^{2}-3\left(x-\frac{1}{x}\right)$
$=\left(x-\frac{1}{x}\right)\left(x-\frac{1}{x}-3\right)$
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