If $x = 3$ and $y = - 1$ , find the values of each of the following using in identity:
$(\frac{3}{x} - \frac{x}{3}) (\frac{x^{2}}{9} + \frac{9}{x^{2}} + 1)$

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Solution

Formula,

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$

Given,

$(\frac{3}{x} - \frac{x}{3}) (\frac{x^{2}}{9} + \frac{9}{x^{2}} + 1)$

$= \frac{27}{x^{3}} - \frac{x^{3}}{27}$

$= \frac{27}{3^{3}} - \frac{3^{3}}{27} = 0$

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