展开 ((1.5)(1+15t^2)^2)/t

解答

展开

\frac{( 1.5 ) ( 1 + 15 t ^{2} ) ^{2}}{t}

\frac{1.5}{t} + 45 t + 337.5 t^{3}

求解步骤

\frac{( 1.5 ) ( 1 + 15 t ^{2} ) ^{2}}{t}

去除括号:

(a) = a

= \frac{1.5 ( 1 + 15 t ^{2} ) ^{2}}{t}

(1 + 15 t^{2})^{2} = 1 + 30 t^{2} + 225 t^{4}

= \frac{1.5 ( 225 t ^{4} + 30 t ^{2} + 1 )}{t}

乘开

1.5 (1 + 30 t^{2} + 225 t^{4}) : 1.5 + 45 t^{2} + 337.5 t^{4}

= \frac{1.5 + 45 t ^{2} + 337.5 t ^{4}}{t}

使用分式法则:

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

\frac{1.5 + 45 t ^{2} + 337.5 t ^{4}}{t} = \frac{1.5}{t} + \frac{45 t ^{2}}{t} + \frac{337.5 t ^{4}}{t}

= \frac{1.5}{t} + \frac{45 t ^{2}}{t} + \frac{337.5 t ^{4}}{t}

消掉

\frac{45 t ^{2}}{t} : 45 t

= \frac{1.5}{t} + 45 t + \frac{337.5 t ^{4}}{t}

消掉

\frac{337.5 t ^{4}}{t} : 337.5 t^{3}

= \frac{1.5}{t} + 45 t + 337.5 t^{3}

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