簡約 (1/a+1/b+1/c)/(1/(ab)+1/(bc)+1/(ac))

解

簡約

\frac{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}}{\frac{1}{ab} + \frac{1}{b c} + \frac{1}{a c}}

\frac{b c + a c + ab}{c + a + b}

解答ステップ

\frac{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}}{\frac{1}{ab} + \frac{1}{b c} + \frac{1}{a c}}

結合

\frac{1}{a} + \frac{1}{b} + \frac{1}{c} : \frac{b c + a c + ab}{ab c}

= \frac{\frac{b c + a c + ab}{ab c}}{\frac{1}{ab} + \frac{1}{b c} + \frac{1}{a c}}

結合

\frac{1}{ab} + \frac{1}{b c} + \frac{1}{a c} : \frac{c + a + b}{ab c}

= \frac{\frac{b c + a c + ab}{ab c}}{\frac{c + a + b}{ab c}}

分数の規則を適用する:

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

= \frac{( b c + a c + ab ) ab c}{ab c ( c + a + b )}

キャンセル

\frac{( b c + a c + ab ) ab c}{ab c ( c + a + b )} : \frac{b c + a c + ab}{c + a + b}

= \frac{b c + a c + ab}{c + a + b}