展開する ((9+x^2)^{11})/(177147x^{11)}

解

展開する

\frac{( 9 + x ^{2} ) ^{11}}{177147 x ^{11}}

\frac{177147}{x ^{11}} + \frac{216513}{x ^{9}} + \frac{120285}{x ^{7}} + \frac{40095}{x ^{5}} + \frac{8910}{x ^{3}} + \frac{1386}{x} + 154 x + \frac{110 x ^{3}}{9} + \frac{55 x ^{5}}{81} + \frac{55 x ^{7}}{2187} + \frac{11 x ^{9}}{19683} + \frac{x ^{11}}{177147}

解答ステップ

\frac{( 9 + x ^{2} ) ^{11}}{177147 x ^{11}}

(9 + x^{2})^{11} = 9^{11} + 9^{10} \cdot 11 x^{2} + 21308126895 x^{4} + 7102708965 x^{6} + 1578379770 x^{8} + 245525742 x^{10} + 27280638 x^{12} + 2165130 x^{14} + 120285 x^{16} + 4455 x^{18} + 99 x^{20} + x^{22}

= \frac{9 ^{11} + 9 ^{10} \cdot 11 x ^{2} + 21308126895 x ^{4} + 7102708965 x ^{6} + 1578379770 x ^{8} + 245525742 x ^{10} + 27280638 x ^{12} + 2165130 x ^{14} + 120285 x ^{16} + 4455 x ^{18} + 99 x ^{20} + x ^{22}}{177147 x ^{11}}

分数の規則を適用する:

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

\frac{9 ^{11} + 9 ^{10} \cdot 11 x ^{2} + 21308126895 x ^{4} + 7102708965 x ^{6} + 1578379770 x ^{8} + 245525742 x ^{10} + 27280638 x ^{12} + 2165130 x ^{14} + 120285 x ^{16} + 4455 x ^{18} + 99 x ^{20} + x ^{22}}{177147 x ^{11}} = \frac{9 ^{11}}{177147 x ^{11}} + \frac{9 ^{10} \cdot 11 x ^{2}}{177147 x ^{11}} + \frac{21308126895 x ^{4}}{177147 x ^{11}} + \frac{7102708965 x ^{6}}{177147 x ^{11}} + \frac{1578379770 x ^{8}}{177147 x ^{11}} + \frac{245525742 x ^{10}}{177147 x ^{11}} + \frac{27280638 x ^{12}}{177147 x ^{11}} + \frac{2165130 x ^{14}}{177147 x ^{11}} + \frac{120285 x ^{16}}{177147 x ^{11}} + \frac{4455 x ^{18}}{177147 x ^{11}} + \frac{99 x ^{20}}{177147 x ^{11}} + \frac{x ^{22}}{177147 x ^{11}}

= \frac{9 ^{11}}{177147 x ^{11}} + \frac{9 ^{10} \cdot 11 x ^{2}}{177147 x ^{11}} + \frac{21308126895 x ^{4}}{177147 x ^{11}} + \frac{7102708965 x ^{6}}{177147 x ^{11}} + \frac{1578379770 x ^{8}}{177147 x ^{11}} + \frac{245525742 x ^{10}}{177147 x ^{11}} + \frac{27280638 x ^{12}}{177147 x ^{11}} + \frac{2165130 x ^{14}}{177147 x ^{11}} + \frac{120285 x ^{16}}{177147 x ^{11}} + \frac{4455 x ^{18}}{177147 x ^{11}} + \frac{99 x ^{20}}{177147 x ^{11}} + \frac{x ^{22}}{177147 x ^{11}}

\frac{9 ^{11}}{177147 x ^{11}} = \frac{177147}{x ^{11}}

\frac{9 ^{10} \cdot 11 x ^{2}}{177147 x ^{11}} = \frac{216513}{x ^{9}}

\frac{21308126895 x ^{4}}{177147 x ^{11}} = \frac{120285}{x ^{7}}

\frac{7102708965 x ^{6}}{177147 x ^{11}} = \frac{40095}{x ^{5}}

\frac{1578379770 x ^{8}}{177147 x ^{11}} = \frac{8910}{x ^{3}}

\frac{245525742 x ^{10}}{177147 x ^{11}} = \frac{1386}{x}

\frac{27280638 x ^{12}}{177147 x ^{11}} = 154 x

\frac{2165130 x ^{14}}{177147 x ^{11}} = \frac{110 x ^{3}}{9}

\frac{120285 x ^{16}}{177147 x ^{11}} = \frac{55 x ^{5}}{81}

\frac{4455 x ^{18}}{177147 x ^{11}} = \frac{55 x ^{7}}{2187}

\frac{99 x ^{20}}{177147 x ^{11}} = \frac{11 x ^{9}}{19683}

\frac{x ^{22}}{177147 x ^{11}} = \frac{x ^{11}}{177147}

= \frac{177147}{x ^{11}} + \frac{216513}{x ^{9}} + \frac{120285}{x ^{7}} + \frac{40095}{x ^{5}} + \frac{8910}{x ^{3}} + \frac{1386}{x} + 154 x + \frac{110 x ^{3}}{9} + \frac{55 x ^{5}}{81} + \frac{55 x ^{7}}{2187} + \frac{11 x ^{9}}{19683} + \frac{x ^{11}}{177147}