展开 (5(x^2(2x^2+3)-36))/(12x^4)

解答

展开

\frac{5 ( x ^{2} ( 2 x ^{2} + 3 ) - 36 )}{12 x ^{4}}

\frac{5}{6} + \frac{5}{4 x ^{2}} - \frac{15}{x ^{4}}

求解步骤

\frac{5 ( x ^{2} ( 2 x ^{2} + 3 ) - 36 )}{12 x ^{4}}

乘开

x^{2} (2 x^{2} + 3) - 36 : 2 x^{4} + 3 x^{2} - 36

= \frac{5 ( 2 x ^{4} + 3 x ^{2} - 36 )}{12 x ^{4}}

乘开

5 (2 x^{4} + 3 x^{2} - 36) : 10 x^{4} + 15 x^{2} - 180

= \frac{10 x ^{4} + 15 x ^{2} - 180}{12 x ^{4}}

使用分式法则:

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

\frac{10 x ^{4} + 15 x ^{2} - 180}{12 x ^{4}} = \frac{10 x ^{4}}{12 x ^{4}} + \frac{15 x ^{2}}{12 x ^{4}} - \frac{180}{12 x ^{4}}

= \frac{10 x ^{4}}{12 x ^{4}} + \frac{15 x ^{2}}{12 x ^{4}} - \frac{180}{12 x ^{4}}

消掉

\frac{10 x ^{4}}{12 x ^{4}} : \frac{5}{6}

= \frac{5}{6} + \frac{15 x ^{2}}{12 x ^{4}} - \frac{180}{12 x ^{4}}

消掉

\frac{15 x ^{2}}{12 x ^{4}} : \frac{5}{4 x ^{2}}

= \frac{5}{6} + \frac{5}{4 x ^{2}} - \frac{180}{12 x ^{4}}

数字相除:

\frac{180}{12} = 15

= \frac{5}{6} + \frac{5}{4 x ^{2}} - \frac{15}{x ^{4}}

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