What is expand-((x-2)(x+2))/x ?

The solution to expand-((x-2)(x+2))/x is -x+4/x

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expand-((x-2)(x+2))/x

expand

- \frac{( x - 2 ) ( x + 2 )}{x}

- x + \frac{4}{x}

Solution steps

- \frac{( x - 2 ) ( x + 2 )}{x}

Expand

(x - 2) (x + 2) : x^{2} - 4

= - \frac{x ^{2} - 4}{x}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{2} - 4}{x} = - (\frac{x ^{2}}{x}) - (- \frac{4}{x})

= - (\frac{x ^{2}}{x}) - (- \frac{4}{x})

Remove parentheses:

(a) = a, - (- a) = a

= - \frac{x ^{2}}{x} + \frac{4}{x}

Cancel

\frac{x ^{2}}{x} : x

= - x + \frac{4}{x}

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