What is ((m^3n^2)/2+7m^{3n})(n/3+1/(mn)) ?

The solution to ((m^3n^2)/2+7m^{3n})(n/3+1/(mn)) is ((14m^{3n}+m^3n^2)(mn^2+3))/(6mn)

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simplify ((m^3n^2)/2+7m^{3n})(n/3+1/(mn))

simplify

(\frac{m ^{3} n ^{2}}{2} + 7 m^{3 n}) (\frac{n}{3} + \frac{1}{mn})

\frac{( 14 m ^{3 n} + m ^{3} n ^{2} ) ( m n ^{2} + 3 )}{6 mn}

Solution steps

(\frac{m ^{3} n ^{2}}{2} + 7 m^{3 n}) (\frac{n}{3} + \frac{1}{mn})

Join

\frac{m ^{3} n ^{2}}{2} + 7 m^{3 n} : \frac{14 m ^{3 n} + m ^{3} n ^{2}}{2}

= \frac{14 m ^{3 n} + m ^{3} n ^{2}}{2} (\frac{n}{3} + \frac{1}{mn})

Apply the fraction rule:

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

= \frac{( 14 m ^{3 n} + m ^{3} n ^{2} ) ( \frac{n}{3} + \frac{1}{mn} )}{2}

Simplify

(14 m^{3 n} + m^{3} n^{2}) (\frac{n}{3} + \frac{1}{mn}) : \frac{( 14 m ^{3 n} + m ^{3} n ^{2} ) ( m n ^{2} + 3 )}{3 mn}

= \frac{\frac{( 14 m ^{3 n} + m ^{3} n ^{2} ) ( m n ^{2} + 3 )}{3 mn}}{2}

Apply the fraction rule:

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

= \frac{( 14 m ^{3 n} + m ^{3} n ^{2} ) ( m n ^{2} + 3 )}{3 mn \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{( 14 m ^{3 n} + m ^{3} n ^{2} ) ( m n ^{2} + 3 )}{6 mn}

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\frac{K ( s ( s + 1 ) ( s + 5 ) )}{1 + K ( s ( s + 1 ) ( s + 5 ) )}

(- 7 + 2 a) \cdot e^{2 a - 4}

\frac{2 ( s ^{2} + 5 )}{s ( s - 4 ) ( s ^{2} + 4 )}

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What is ((m^3n^2)/2+7m^{3n})(n/3+1/(mn)) ?
The solution to ((m^3n^2)/2+7m^{3n})(n/3+1/(mn)) is ((14m^{3n}+m^3n^2)(mn^2+3))/(6mn)