化简 (n-(m^2)/n)((n^2)/m-m)

解答

化简

(n - \frac{m ^{2}}{n}) (\frac{n ^{2}}{m} - m)

\frac{( n ^{2} - m ^{2} ) ^{2}}{mn}

求解步骤

(n - \frac{m ^{2}}{n}) (\frac{n ^{2}}{m} - m)

合并

n - \frac{m ^{2}}{n} : \frac{n ^{2} - m ^{2}}{n}

= \frac{n ^{2} - m ^{2}}{n} (\frac{n ^{2}}{m} - m)

使用分式法则:

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

= \frac{( n ^{2} - m ^{2} ) ( \frac{n ^{2}}{m} - m )}{n}

化简

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

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

使用分式法则:

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

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

化简

(n^{2} - m^{2}) (- m^{2} + n^{2}) : (n^{2} - m^{2})^{2}

= \frac{( n ^{2} - m ^{2} ) ^{2}}{mn}

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