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

Lösung

erweitern

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

\frac{1}{s ^{3} + 2 b s ^{2} + b ^{2} s + a s ^{2} + 2 ab s + a b ^{2}}

Schritte zur Lösung

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

(s + b)^{2} = s^{2} + 2 b s + b^{2}

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

Multipliziere aus

(s + a) (s^{2} + 2 s b + b^{2}) : s^{3} + 2 b s^{2} + b^{2} s + a s^{2} + 2 ab s + a b^{2}

= \frac{1}{s ^{3} + 2 b s ^{2} + b ^{2} s + a s ^{2} + 2 ab s + a b ^{2}}

e x p an d \frac{3 ( x + 2 )}{5}

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

e x p an d \frac{1 - e ^{- 2 π s}}{( s ^{2} + 1 ) ( s ^{2} + 4 )}

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

e x p an d a^{2} + (x + Δ x)^{2} - a^{2} + x^{2}