erweitern (4s+2s^2-8)/((s+2)^2(s-2)^2)

Lösung

erweitern

\frac{4 s + 2 s ^{2} - 8}{( s + 2 ) ^{2} ( s - 2 ) ^{2}}

\frac{4 s + 2 s ^{2} - 8}{s ^{4} - 8 s ^{2} + 16}

Schritte zur Lösung

\frac{4 s + 2 s ^{2} - 8}{( s + 2 ) ^{2} ( s - 2 ) ^{2}}

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

= \frac{4 s + 2 s ^{2} - 8}{( s ^{2} + 4 s + 4 ) ( s - 2 ) ^{2}}

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

= \frac{4 s + 2 s ^{2} - 8}{( s ^{2} + 4 s + 4 ) ( s ^{2} - 4 s + 4 )}

Multipliziere aus

(s^{2} + 4 s + 4) (s^{2} - 4 s + 4) : s^{4} - 8 s^{2} + 16

= \frac{4 s + 2 s ^{2} - 8}{s ^{4} - 8 s ^{2} + 16}

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

e x p an d tan (x) (cot (x) + csc (x))

e x p an d (x + \frac{1}{x})^{5}

s im pl i f y (2 x - \frac{1}{2}) (2 x + \frac{1}{2})

s im pl i f y \frac{1}{( 2 - 3 i ) ^{5}}