展开 (64(s+10)(s+50))/((s)^2(s+100)^2(s+400))

解答

展开

\frac{64 ( s + 10 ) ( s + 50 )}{( s ) ^{2} ( s + 100 ) ^{2} ( s + 400 )}

\frac{64 s ^{2} + 3840 s + 32000}{s ^{5} + 600 s ^{4} + 90000 s ^{3} + 4000000 s ^{2}}

求解步骤

\frac{64 ( s + 10 ) ( s + 50 )}{s ^{2} ( s + 100 ) ^{2} ( s + 400 )}

(s + 100)^{2} = s^{2} + 200 s + 10000

= \frac{64 ( s + 10 ) ( s + 50 )}{s ^{2} ( s ^{2} + 200 s + 10000 ) ( s + 400 )}

乘开

s^{2} (s^{2} + 200 s + 10000) (s + 400) : s^{5} + 600 s^{4} + 90000 s^{3} + 4000000 s^{2}

= \frac{64 ( s + 10 ) ( s + 50 )}{s ^{5} + 600 s ^{4} + 90000 s ^{3} + 4000000 s ^{2}}

乘开

64 (s + 10) (s + 50) : 64 s^{2} + 3840 s + 32000

= \frac{64 s ^{2} + 3840 s + 32000}{s ^{5} + 600 s ^{4} + 90000 s ^{3} + 4000000 s ^{2}}

s im pl i f y (8 - x + 7)^{2}

e x p an d \frac{4 ( 2 n + 4 )}{n}

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

e x p an d \frac{1}{25} (- 5 t + e^{5 t} - 1)

e x p an d \frac{\frac{4 x}{x + 1}}{\frac{3 x ^{4}}{x ^{2} - 1}}