erweitern (s^2+3s+4b)/((s+2)^3(s+1)(s+a))

Lösung

erweitern

\frac{s ^{2} + 3 s + 4 b}{( s + 2 ) ^{3} ( s + 1 ) ( s + a )}

\frac{s ^{2} + 3 s + 4 b}{s ^{5} + a s ^{4} + 7 s ^{4} + 7 a s ^{3} + 18 s ^{3} + 18 a s ^{2} + 20 s ^{2} + 20 a s + 8 s + 8 a}

Schritte zur Lösung

\frac{s ^{2} + 3 s + 4 b}{( s + 2 ) ^{3} ( s + 1 ) ( s + a )}

(s + 2)^{3} = s^{3} + 6 s^{2} + 12 s + 8

= \frac{s ^{2} + 3 s + 4 b}{( s ^{3} + 6 s ^{2} + 12 s + 8 ) ( s + 1 ) ( s + a )}

Multipliziere aus

(s^{3} + 6 s^{2} + 12 s + 8) (s + 1) (s + a) : s^{5} + a s^{4} + 7 s^{4} + 7 a s^{3} + 18 s^{3} + 18 a s^{2} + 20 s^{2} + 20 a s + 8 s + 8 a

= \frac{s ^{2} + 3 s + 4 b}{s ^{5} + a s ^{4} + 7 s ^{4} + 7 a s ^{3} + 18 s ^{3} + 18 a s ^{2} + 20 s ^{2} + 20 a s + 8 s + 8 a}

e x p an d e^{9 (a - jω)}

e x p an d \frac{1}{( 1 - a ) ( 1 - b )}

e x p an d \frac{( x + 10 ) ( 2 x - 1 )}{( x + 2 ) ( x - 1 )}

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

e x p an d \frac{1}{( 2 x + 7 ) ^{9}}