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Properties of Square Numbers

Evaluate x-...

Question

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

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Solution

${(x - \frac{1}{x})}^{2} - {(x + \frac{1}{x})}^{2}$
$\Rightarrow x^{2} + \frac{1}{x^{2}} - 2 - (x^{2} + \frac{1}{x^{2}} + 2)$
$\Rightarrow x^{2} + \frac{1}{x^{2}} - 2 - x^{2} - \frac{1}{x^{2}} - 2$
$\Rightarrow - 4$ .

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