展开 (5x^3+14x^2+23x+6)/((s+3)(s-3)(s+1)^2)

解答

展开

\frac{5 x ^{3} + 14 x ^{2} + 23 x + 6}{( s + 3 ) \cdot ( s - 3 ) \cdot ( s + 1 ) ^{2}}

\frac{5 x ^{3} + 14 x ^{2} + 23 x + 6}{s ^{4} + 2 s ^{3} - 8 s ^{2} - 18 s - 9}

求解步骤

\frac{5 x ^{3} + 14 x ^{2} + 23 x + 6}{( s + 3 ) ( s - 3 ) ( s + 1 ) ^{2}}

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

= \frac{5 x ^{3} + 14 x ^{2} + 23 x + 6}{( s + 3 ) ( s - 3 ) ( s ^{2} + 2 s + 1 )}

乘开

(s + 3) (s - 3) (s^{2} + 2 s + 1) : s^{4} + 2 s^{3} - 8 s^{2} - 18 s - 9

= \frac{5 x ^{3} + 14 x ^{2} + 23 x + 6}{s ^{4} + 2 s ^{3} - 8 s ^{2} - 18 s - 9}

s im pl i f y 1 + \frac{1}{s ( s + 2.2 )}

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

e x p an d \frac{1}{( s + 2 ) ( s + 3 )}

\frac{d}{d z} ((w) (3 z^{7} - 7 z^{3} + 21 z^{2}))

e x p an d e^{x (x - 9)}