簡約 1/((s-i)^3)+1/((s+i)^3)

解

簡約

\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}

解答ステップ

\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}

結合

\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}