erweitern (s^3+2s^2+4s+5)/((s+1)^2(s+2)^2)

Lösung

erweitern

\frac{s ^{3} + 2 s ^{2} + 4 s + 5}{( s + 1 ) ^{2} ( s + 2 ) ^{2}}

\frac{s ^{3} + 2 s ^{2} + 4 s + 5}{s ^{4} + 6 s ^{3} + 13 s ^{2} + 12 s + 4}

Schritte zur Lösung

\frac{s ^{3} + 2 s ^{2} + 4 s + 5}{( s + 1 ) ^{2} ( s + 2 ) ^{2}}

(s + 1)^{2} = s^{2} + 2 s + 1

= \frac{s ^{3} + 2 s ^{2} + 4 s + 5}{( s ^{2} + 2 s + 1 ) ( s + 2 ) ^{2}}

(s + 2)^{2} = s^{2} + 4 s + 4

= \frac{s ^{3} + 2 s ^{2} + 4 s + 5}{( s ^{2} + 2 s + 1 ) ( s ^{2} + 4 s + 4 )}

Multipliziere aus

(s^{2} + 2 s + 1) (s^{2} + 4 s + 4) : s^{4} + 6 s^{3} + 13 s^{2} + 12 s + 4

= \frac{s ^{3} + 2 s ^{2} + 4 s + 5}{s ^{4} + 6 s ^{3} + 13 s ^{2} + 12 s + 4}

e x p an d (5 x^{3} - e^{4 x})^{2}

e x p an d 2 \cdot 1.97 \cdot (1, 7 - 0)

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

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

e x p an d \frac{8}{s ^{3} ( s ^{2} - s - 2 )}