vereinfachen 1/((s-i)^3)+1/((s+i)^3)

Lösung

vereinfachen

\frac{1}{( s - i ) ^{3}} + \frac{1}{( s + i ) ^{3}}

\frac{2 s ^{3} - 6 s}{s ^{6} + 3 s ^{4} + 3 s ^{2} + 1}

Schritte zur Lösung

\frac{1}{( s - i ) ^{3}} + \frac{1}{( s + i ) ^{3}}

\frac{1}{( s - i ) ^{3}} = \frac{s ^{3} - 3 s + i ( 3 s ^{2} - 1 )}{s ^{6} + 3 s ^{4} + 3 s ^{2} + 1}

\frac{1}{( s + i ) ^{3}} = \frac{s ^{3} - 3 s + i ( - 3 s ^{2} + 1 )}{s ^{6} + 3 s ^{4} + 3 s ^{2} + 1}

= \frac{s ^{3} - 3 s + i ( 3 s ^{2} - 1 )}{s ^{6} + 3 s ^{4} + 3 s ^{2} + 1} + \frac{s ^{3} - 3 s + i ( - 3 s ^{2} + 1 )}{s ^{6} + 3 s ^{4} + 3 s ^{2} + 1}

Füge zusammen:

\frac{s ^{3} - 3 s + i ( 3 s ^{2} - 1 )}{s ^{6} + 3 s ^{4} + 3 s ^{2} + 1} + \frac{s ^{3} - 3 s + i ( - 3 s ^{2} + 1 )}{s ^{6} + 3 s ^{4} + 3 s ^{2} + 1} : \frac{2 s ^{3} - 6 s}{s ^{6} + 3 s ^{4} + 3 s ^{2} + 1}

= \frac{2 s ^{3} - 6 s}{s ^{6} + 3 s ^{4} + 3 s ^{2} + 1}

e x p an d \frac{1}{( s + 5 ) ( s - 4 )}

e x p an d (4 x^{3} + 5) \cdot (x^{4} + 5 x)^{\frac{1}{2}}

e x p an d ((X - 4) X - 1) \cdot (53 + 5 X - 1)

e x p an d \frac{( 1 + 3 j ) ( 1 + 7 j )}{( 7 - 9 j ) ( 2 - j )}

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