簡約 1+1/((0.3s+1)(s+1)(1.2s+1))

解

簡約

1 + \frac{1}{( 0.3 s + 1 ) \cdot ( s + 1 ) \cdot ( 1.2 s + 1 )}

\frac{0.36 s ^{3} + 1.86 s ^{2} + 2.5 s + 2}{( 0.3 s + 1 ) ( s + 1 ) ( 1.2 s + 1 )}

解答ステップ

1 + \frac{1}{( 0.3 s + 1 ) ( s + 1 ) ( 1.2 s + 1 )}

分数の規則を適用する:

1 + \frac{b}{c} = \frac{c + b}{c}

= \frac{( 0.3 s + 1 ) ( s + 1 ) ( 1.2 s + 1 ) + 1}{( 0.3 s + 1 ) ( s + 1 ) ( 1.2 s + 1 )}

簡素化

(0.3 s + 1) (s + 1) (1.2 s + 1) + 1 : 0.36 s^{3} + 1.86 s^{2} + 2.5 s + 2

= \frac{0.36 s ^{3} + 1.86 s ^{2} + 2.5 s + 2}{( 0.3 s + 1 ) ( s + 1 ) ( 1.2 s + 1 )}