What is expand (k(s+3))/((s+5)(s+1)^2) ?

The solution to expand (k(s+3))/((s+5)(s+1)^2) is (ks+3k)/(s^3+7s^2+11s+5)

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expand (k(s+3))/((s+5)(s+1)^2)

expand

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

\frac{k s + 3 k}{s ^{3} + 7 s ^{2} + 11 s + 5}

Solution steps

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

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

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

Expand

(s + 5) (s^{2} + 2 s + 1) : s^{3} + 7 s^{2} + 11 s + 5

= \frac{k ( s + 3 )}{s ^{3} + 7 s ^{2} + 11 s + 5}

Expand

k (s + 3) : k s + 3 k

= \frac{k s + 3 k}{s ^{3} + 7 s ^{2} + 11 s + 5}

7 (3 - 7)

2^{(n + 1)^{2}}

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

(1 + 2 sin (θ))^{2}

What is expand (k(s+3))/((s+5)(s+1)^2) ?
The solution to expand (k(s+3))/((s+5)(s+1)^2) is (ks+3k)/(s^3+7s^2+11s+5)