What is ((4/n-n))/((1/n+1/2)) ?

The solution to ((4/n-n))/((1/n+1/2)) is -2n+4

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simplify ((4/n-n))/((1/n+1/2))

simplify

\frac{( \frac{4}{n} - n )}{( \frac{1}{n} + \frac{1}{2} )}

- 2 n + 4

Solution steps

\frac{\frac{4}{n} - n}{\frac{1}{n} + \frac{1}{2}}

Join

\frac{4}{n} - n : \frac{- n ^{2} + 4}{n}

= \frac{\frac{- n ^{2} + 4}{n}}{\frac{1}{n} + \frac{1}{2}}

Join

\frac{1}{n} + \frac{1}{2} : \frac{2 + n}{2 n}

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

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( - n ^{2} + 4 ) \cdot 2 n}{n ( 2 + n )}

Cancel

\frac{( - n ^{2} + 4 ) \cdot 2 n}{n ( 2 + n )} : - (n - 2) \cdot 2

= - (n - 2) \cdot 2

Expand

- (n - 2) \cdot 2 : - 2 n + 4

= - 2 n + 4

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