展开 ((s+1)^3)/(s^5)

解答

展开

\frac{( s + 1 ) ^{3}}{s ^{5}}

\frac{1}{s ^{2}} + \frac{3}{s ^{3}} + \frac{3}{s ^{4}} + \frac{1}{s ^{5}}

求解步骤

\frac{( s + 1 ) ^{3}}{s ^{5}}

(s + 1)^{3} = s^{3} + 3 s^{2} + 3 s + 1

= \frac{s ^{3} + 3 s ^{2} + 3 s + 1}{s ^{5}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{s ^{3} + 3 s ^{2} + 3 s + 1}{s ^{5}} = \frac{s ^{3}}{s ^{5}} + \frac{3 s ^{2}}{s ^{5}} + \frac{3 s}{s ^{5}} + \frac{1}{s ^{5}}

= \frac{s ^{3}}{s ^{5}} + \frac{3 s ^{2}}{s ^{5}} + \frac{3 s}{s ^{5}} + \frac{1}{s ^{5}}

消掉

\frac{s ^{3}}{s ^{5}} : \frac{1}{s ^{2}}

= \frac{1}{s ^{2}} + \frac{3 s ^{2}}{s ^{5}} + \frac{3 s}{s ^{5}} + \frac{1}{s ^{5}}

消掉

\frac{3 s ^{2}}{s ^{5}} : \frac{3}{s ^{3}}

= \frac{1}{s ^{2}} + \frac{3}{s ^{3}} + \frac{3 s}{s ^{5}} + \frac{1}{s ^{5}}

消掉

\frac{3 s}{s ^{5}} : \frac{3}{s ^{4}}

= \frac{1}{s ^{2}} + \frac{3}{s ^{3}} + \frac{3}{s ^{4}} + \frac{1}{s ^{5}}

e x p an d (1 - x) e^{x}

e x p an d ln (a + 1) \cdot (e^{a} + a \cdot e^{a})

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

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

e x p an d e^{k t} (5 - b t + 4 sin (\frac{t}{a}))