What is expand ((s+1)^2+1)/((s+2)(s+1)^2) ?

The solution to expand ((s+1)^2+1)/((s+2)(s+1)^2) is (s^2+2s+2)/(s^3+4s^2+5s+2)

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expand ((s+1)^2+1)/((s+2)(s+1)^2)

expand

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

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

Solution steps

\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 )}

Expand

(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}

Expand

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

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

x (3 x - 10) - 31 + 1

18 (\frac{9}{44} + \frac{3 ln ( \frac{11}{8} )}{4})

5 \cdot (\frac{π}{4} + 2 π)

(s + \frac{b}{m}) (s + \frac{r}{l})

(20 - e^{0.05 x}) x

What is expand ((s+1)^2+1)/((s+2)(s+1)^2) ?
The solution to expand ((s+1)^2+1)/((s+2)(s+1)^2) is (s^2+2s+2)/(s^3+4s^2+5s+2)