簡約 (c^2+4c)/(c^2-4)*(c-2)/(3c+12)

解

簡約

\frac{c ^{2} + 4 c}{c ^{2} - 4} \cdot \frac{c - 2}{3 c + 12}

\frac{c}{3 ( c + 2 )}

解答ステップ

\frac{c ^{2} + 4 c}{c ^{2} - 4} \cdot \frac{c - 2}{3 c + 12}

分数の規則を適用する:

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

= \frac{( c ^{2} + 4 c ) ( c - 2 )}{( c ^{2} - 4 ) ( 3 c + 12 )}

因数

c^{2} - 4 : (c + 2) (c - 2)

= \frac{( c ^{2} + 4 c ) ( c - 2 )}{( c + 2 ) ( c - 2 ) ( 3 c + 12 )}

共通因数を約分する:

c - 2

= \frac{c ^{2} + 4 c}{( c + 2 ) ( 3 c + 12 )}

因数

c^{2} + 4 c : c (c + 4)

= \frac{c ( c + 4 )}{( c + 2 ) ( 3 c + 12 )}

因数

3 c + 12 : 3 (c + 4)

= \frac{c ( c + 4 )}{( c + 2 ) \cdot 3 ( c + 4 )}

共通因数を約分する:

c + 4

= \frac{c}{( c + 2 ) \cdot 3}

= \frac{c}{3 ( c + 2 )}