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

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

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

expand

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

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

Solution steps

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

Distribute parentheses

= 1 \cdot \frac{s}{s ^{2} + 1} + 1 \cdot s + 1 \cdot 1 + \frac{1}{s} \cdot \frac{s}{s ^{2} + 1} + \frac{1}{s} s + \frac{1}{s} \cdot 1

Simplify

1 \cdot \frac{s}{s ^{2} + 1} + 1 \cdot s + 1 \cdot 1 + \frac{1}{s} \cdot \frac{s}{s ^{2} + 1} + \frac{1}{s} s + \frac{1}{s} \cdot 1 : s + \frac{s + 1}{s ^{2} + 1} + \frac{1}{s} + 2

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

2 (ln (3) - 2 + \frac{2}{3})

\frac{x + 5}{( x + 1 ) ^{2} ( x + 3 )}

e^{64 + 48 k} \cdot (48 - 24 k)

e^{\frac{t}{2} + c} ((- \frac{2}{3} e^{c} (e^{- \frac{3 t}{2}} - 1)) + c)

\frac{( x + 2 ) ^{2} \cdot ( x - 1 ) ( x + 1 )}{2 x ^{2} - 7 x - 4}

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