展開する ((9x^2-3)(x+3)(x^2+5))/(x^4)

解

展開する

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

9 x + 27 + \frac{42}{x} + \frac{126}{x ^{2}} - \frac{15}{x ^{3}} - \frac{45}{x ^{4}}

解答ステップ

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

拡張

(9 x^{2} - 3) (x + 3) (x^{2} + 5) : 9 x^{5} + 27 x^{4} + 42 x^{3} + 126 x^{2} - 15 x - 45

= \frac{9 x ^{5} + 27 x ^{4} + 42 x ^{3} + 126 x ^{2} - 15 x - 45}{x ^{4}}

分数の規則を適用する:

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

\frac{9 x ^{5} + 27 x ^{4} + 42 x ^{3} + 126 x ^{2} - 15 x - 45}{x ^{4}} = \frac{9 x ^{5}}{x ^{4}} + \frac{27 x ^{4}}{x ^{4}} + \frac{42 x ^{3}}{x ^{4}} + \frac{126 x ^{2}}{x ^{4}} - \frac{15 x}{x ^{4}} - \frac{45}{x ^{4}}

= \frac{9 x ^{5}}{x ^{4}} + \frac{27 x ^{4}}{x ^{4}} + \frac{42 x ^{3}}{x ^{4}} + \frac{126 x ^{2}}{x ^{4}} - \frac{15 x}{x ^{4}} - \frac{45}{x ^{4}}

\frac{9 x ^{5}}{x ^{4}} = 9 x

\frac{27 x ^{4}}{x ^{4}} = 27

\frac{42 x ^{3}}{x ^{4}} = \frac{42}{x}

\frac{126 x ^{2}}{x ^{4}} = \frac{126}{x ^{2}}

\frac{15 x}{x ^{4}} = \frac{15}{x ^{3}}

= 9 x + 27 + \frac{42}{x} + \frac{126}{x ^{2}} - \frac{15}{x ^{3}} - \frac{45}{x ^{4}}