簡約 (\frac{c^2-4)/(c+3)}{(c+2)/(3(c^2-9))}

解

簡約

\frac{\frac{c ^{2} - 4}{c + 3}}{\frac{c + 2}{3 ( c ^{2} - 9 )}}

3 (c - 2) (c - 3)

解答ステップ

\frac{\frac{c ^{2} - 4}{c + 3}}{\frac{c + 2}{3 ( c ^{2} - 9 )}}

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 ^{2} - 4 ) \cdot 3 ( c ^{2} - 9 )}{( c + 3 ) ( c + 2 )}

キャンセル

\frac{( c ^{2} - 4 ) \cdot 3 ( c ^{2} - 9 )}{( c + 3 ) ( c + 2 )} : (c - 2) \cdot 3 (c - 3)

= (c - 2) \cdot 3 (c - 3)

= 3 (c - 2) (c - 3)