化简 (k(s+1.5))/(s(s+1)(s+10)+1.5k)

解答

化简

\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}

求解步骤

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

Apply FOIL method

(s + 1) (s + 10) : s^{2} + 11 s + 10

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

使用分配律:

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}

化简

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}

s im pl i f y (x + i y - a - bi)^{2}

e x p an d \frac{sin ^{2} ( ( x + 2 ) ( x - 2 ) )}{( x + 2 ) ( x - 2 )}

e x p an d \frac{z ^{3}}{( z + 1 ) ( z - 1 ) ^{2}}

e x p an d (1 + sin (x)) (1 - cos (x))

s im pl i f y sec^{2} (\frac{x}{2}) + 3 (x - 10)^{2} + \frac{2}{x ^{4}}