簡約 (2a)/(9-a^2)*(a-3)/(a^3+a)

解

簡約

\frac{2 a}{9 - a ^{2}} \cdot \frac{a - 3}{a ^{3} + a}

- \frac{2}{( 3 + a ) ( a ^{2} + 1 )}

解答ステップ

\frac{2 a}{9 - a ^{2}} \cdot \frac{a - 3}{a ^{3} + a}

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{2 a ( a - 3 )}{( 9 - a ^{2} ) ( a ^{3} + a )}

因数

9 - a^{2} : (3 + a) (3 - a)

= \frac{2 a ( a - 3 )}{( 3 + a ) ( 3 - a ) ( a ^{3} + a )}

(3 + a) (3 - a) (a^{3} + a) = - (3 + a) (a - 3) (a^{3} + a)

= \frac{2 a ( a - 3 )}{- ( 3 + a ) ( a - 3 ) ( a ^{3} + a )}

共通因数を約分する:

a - 3

= \frac{2 a}{- ( 3 + a ) ( a ^{3} + a )}

因数

a^{3} + a : a (a^{2} + 1)

= \frac{2 a}{- ( 3 + a ) a ( a ^{2} + 1 )}

共通因数を約分する:

a

= \frac{2}{- ( 3 + a ) ( a ^{2} + 1 )}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2}{( 3 + a ) ( a ^{2} + 1 )}