展开 ((s^2+9s+7))/((s^2+7s+9)(s-7)^2)

解答

展开

\frac{( s ^{2} + 9 s + 7 )}{( s ^{2} + 7 s + 9 ) ( s - 7 ) ^{2}}

\frac{s ^{2} + 9 s + 7}{s ^{4} - 7 s ^{3} - 40 s ^{2} + 217 s + 441}

求解步骤

\frac{s ^{2} + 9 s + 7}{( s ^{2} + 7 s + 9 ) ( s - 7 ) ^{2}}

(s - 7)^{2} = s^{2} - 14 s + 49

= \frac{s ^{2} + 9 s + 7}{( s ^{2} + 7 s + 9 ) ( s ^{2} - 14 s + 49 )}

乘开

(s^{2} + 7 s + 9) (s^{2} - 14 s + 49) : s^{4} - 7 s^{3} - 40 s^{2} + 217 s + 441

= \frac{s ^{2} + 9 s + 7}{s ^{4} - 7 s ^{3} - 40 s ^{2} + 217 s + 441}

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

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

e x p an d - \frac{( - 1 ) ^{n} - 1}{π ^{2} n ^{2}}

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

e x p an d x^{2} d v (v - v x^{2} d v)