What is ((m+n))/((2/m+2/n)) ?

The solution to ((m+n))/((2/m+2/n)) is (mn)/2

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simplify ((m+n))/((2/m+2/n))

simplify

\frac{( m + n )}{( \frac{2}{m} + \frac{2}{n} )}

\frac{mn}{2}

Solution steps

\frac{m + n}{\frac{2}{m} + \frac{2}{n}}

Join

\frac{2}{m} + \frac{2}{n} : \frac{2 n + 2 m}{mn}

= \frac{m + n}{\frac{2 n + 2 m}{mn}}

Apply the fraction rule:

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

= \frac{( m + n ) mn}{2 n + 2 m}

Cancel

\frac{( m + n ) mn}{2 n + 2 m} : \frac{mn}{2}

= \frac{mn}{2}

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