展开 (2x+5(5x^4-2))/x

解答

展开

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

2 + 25 x^{3} - \frac{10}{x}

求解步骤

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

乘开

2 x + 5 (5 x^{4} - 2) : 2 x + 25 x^{4} - 10

= \frac{2 x + 25 x ^{4} - 10}{x}

使用分式法则:

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

\frac{2 x + 25 x ^{4} - 10}{x} = \frac{2 x}{x} + \frac{25 x ^{4}}{x} - \frac{10}{x}

= \frac{2 x}{x} + \frac{25 x ^{4}}{x} - \frac{10}{x}

消掉

\frac{2 x}{x} : 2

= 2 + \frac{25 x ^{4}}{x} - \frac{10}{x}

消掉

\frac{25 x ^{4}}{x} : 25 x^{3}

= 2 + 25 x^{3} - \frac{10}{x}

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