展開する-(4(x^2+4x+2))/(9x^{5/3)(x+2)^{8/3}}

解

展開する

- \frac{4 ( x ^{2} + 4 x + 2 )}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}

- \frac{4 x ^{\frac{1}{3}}}{9 ( x + 2 ) ^{\frac{8}{3}}} - \frac{16}{9 x ^{\frac{2}{3}} ( x + 2 ) ^{\frac{8}{3}}} - \frac{8}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}

解答ステップ

- \frac{4 ( x ^{2} + 4 x + 2 )}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}

拡張

4 (x^{2} + 4 x + 2) : 4 x^{2} + 16 x + 8

= - \frac{4 x ^{2} + 16 x + 8}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{4 x ^{2} + 16 x + 8}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}} = - (\frac{4 x ^{2}}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}) - (\frac{16 x}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}) - (\frac{8}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}})

= - (\frac{4 x ^{2}}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}) - (\frac{16 x}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}) - (\frac{8}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}})

括弧を削除する:

(a) = a

= - \frac{4 x ^{2}}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}} - \frac{16 x}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}} - \frac{8}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}

キャンセル

\frac{4 x ^{2}}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}} : \frac{4 x ^{\frac{1}{3}}}{9 ( x + 2 ) ^{\frac{8}{3}}}

= - \frac{4 x ^{\frac{1}{3}}}{9 ( x + 2 ) ^{\frac{8}{3}}} - \frac{16 x}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}} - \frac{8}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}

キャンセル

\frac{16 x}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}} : \frac{16}{9 x ^{\frac{2}{3}} ( x + 2 ) ^{\frac{8}{3}}}

= - \frac{4 x ^{\frac{1}{3}}}{9 ( x + 2 ) ^{\frac{8}{3}}} - \frac{16}{9 x ^{\frac{2}{3}} ( x + 2 ) ^{\frac{8}{3}}} - \frac{8}{9 x ^{\frac{5}{3}} ( x + 2 ) ^{\frac{8}{3}}}