展开 ((a^2+9)(a^2-3)3)/(4a^2)

解答

展开

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

\frac{3 a ^{2}}{4} + \frac{9}{2} - \frac{81}{4 a ^{2}}

求解步骤

\frac{( a ^{2} + 9 ) ( a ^{2} - 3 ) \cdot 3}{4 a ^{2}}

乘开

(a^{2} + 9) (a^{2} - 3) \cdot 3 : 3 a^{4} + 18 a^{2} - 81

= \frac{3 a ^{4} + 18 a ^{2} - 81}{4 a ^{2}}

使用分式法则:

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

\frac{3 a ^{4} + 18 a ^{2} - 81}{4 a ^{2}} = \frac{3 a ^{4}}{4 a ^{2}} + \frac{18 a ^{2}}{4 a ^{2}} - \frac{81}{4 a ^{2}}

= \frac{3 a ^{4}}{4 a ^{2}} + \frac{18 a ^{2}}{4 a ^{2}} - \frac{81}{4 a ^{2}}

消掉

\frac{3 a ^{4}}{4 a ^{2}} : \frac{3 a ^{2}}{4}

= \frac{3 a ^{2}}{4} + \frac{18 a ^{2}}{4 a ^{2}} - \frac{81}{4 a ^{2}}

消掉

\frac{18 a ^{2}}{4 a ^{2}} : \frac{9}{2}

= \frac{3 a ^{2}}{4} + \frac{9}{2} - \frac{81}{4 a ^{2}}

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