簡約 (c+\frac{125)/(c^2)}{1+5/c}

解

簡約

\frac{c + \frac{125}{c ^{2}}}{1 + \frac{5}{c}}

\frac{c ^{2} - 5 c + 25}{c}

解答ステップ

\frac{c + \frac{125}{c ^{2}}}{1 + \frac{5}{c}}

結合

c + \frac{125}{c ^{2}} : \frac{c ^{3} + 125}{c ^{2}}

= \frac{\frac{c ^{3} + 125}{c ^{2}}}{1 + \frac{5}{c}}

結合

1 + \frac{5}{c} : \frac{c + 5}{c}

= \frac{\frac{c ^{3} + 125}{c ^{2}}}{\frac{c + 5}{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{( c ^{3} + 125 ) c}{c ^{2} ( c + 5 )}

キャンセル

\frac{( c ^{3} + 125 ) c}{c ^{2} ( c + 5 )} : \frac{c ^{2} - 5 c + 25}{c}

= \frac{c ^{2} - 5 c + 25}{c}