展开 ((s+1)^2+1)/((s+2)(s+1)^2)

解答

展开

\frac{( s + 1 ) ^{2} + 1}{( s + 2 ) ( s + 1 ) ^{2}}

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

求解步骤

\frac{( s + 1 ) ^{2} + 1}{( s + 2 ) ( s + 1 ) ^{2}}

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

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

乘开

(s + 2) (s^{2} + 2 s + 1) : s^{3} + 4 s^{2} + 5 s + 2

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

乘开

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

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

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