Question
Simplify$:\left(x-\frac{1}{x}\right)\left(x^2+1+\frac{1}{x^2}\right)$
✓
Answer
$\left(x-\frac{1}{x}\right)\left(x^2+1+\frac{1}{x^2}\right) $
$ =x\left(x^2+1+\frac{1}{x^2}\right)-\frac{1}{x}\left(x^2+1+\frac{1}{x^2}\right) $
$ =x^3+x+\frac{1}{x}-x-\frac{1}{x}-\frac{1}{x^3}$
$=x^3-\frac{1}{x^3} .$
$ =x\left(x^2+1+\frac{1}{x^2}\right)-\frac{1}{x}\left(x^2+1+\frac{1}{x^2}\right) $
$ =x^3+x+\frac{1}{x}-x-\frac{1}{x}-\frac{1}{x^3}$
$=x^3-\frac{1}{x^3} .$
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