展开 1.2538((1+0.16s)(1+0.16s))/s

解答

展开

1.2538 \frac{( 1 + 0.16 s ) ( 1 + 0.16 s )}{s}

\frac{1.2538}{s} + 0.401216 + 0.03209728 s

求解步骤

1.2538 \cdot \frac{( 1 + 0.16 s ) ( 1 + 0.16 s )}{s}

\frac{( 1 + 0.16 s ) ( 1 + 0.16 s )}{s} = \frac{1 + 0.32 s + 0.0256 s ^{2}}{s}

= 1.2538 \cdot \frac{0.0256 s ^{2} + 0.32 s + 1}{s}

分式相乘:

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

= \frac{( 1 + 0.32 s + 0.0256 s ^{2} ) \cdot 1.2538}{s}

乘开

(1 + 0.32 s + 0.0256 s^{2}) \cdot 1.2538 : 1.2538 + 0.401216 s + 0.03209728 s^{2}

= \frac{1.2538 + 0.401216 s + 0.03209728 s ^{2}}{s}

使用分式法则:

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

\frac{1.2538 + 0.401216 s + 0.03209728 s ^{2}}{s} = \frac{1.2538}{s} + \frac{0.401216 s}{s} + \frac{0.03209728 s ^{2}}{s}

= \frac{1.2538}{s} + \frac{0.401216 s}{s} + \frac{0.03209728 s ^{2}}{s}

消掉

\frac{0.401216 s}{s} : 0.401216

= \frac{1.2538}{s} + 0.401216 + \frac{0.03209728 s ^{2}}{s}

消掉

\frac{0.03209728 s ^{2}}{s} : 0.03209728 s

= \frac{1.2538}{s} + 0.401216 + 0.03209728 s

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