簡約 (k(s+1.5))/(s(s+1)(s+10)+1.5k)

解

簡約

\frac{k ( s + 1.5 )}{s ( s + 1 ) ( s + 10 ) + 1.5 k}

\frac{k ( s + 1.5 )}{s ^{3} + 11 s ^{2} + 10 s + 1.5 k}

解答ステップ

\frac{k ( s + 1.5 )}{s ( s + 1 ) ( s + 10 ) + 1.5 k}

FOIL方法

(s + 1) (s + 10)

を適用します:

s^{2} + 11 s + 10

= \frac{k ( s + 1.5 )}{s ( s ^{2} + 11 s + 10 ) + 1.5 k}

分配法則を適用する:

m (a + b + c) = ma + mb + m c

s (s^{2} + 11 s + 10) = s s^{2} + s \cdot 11 s + s \cdot 10

= \frac{k ( s + 1.5 )}{s s ^{2} + s \cdot 11 s + s \cdot 10 + 1.5 k}

簡素化

s s^{2} + s \cdot 11 s + s \cdot 10 : s^{3} + 11 s^{2} + 10 s

= \frac{k ( s + 1.5 )}{s ^{3} + 11 s ^{2} + 10 s + 1.5 k}