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

The solution to expand (k(s+1)(s+2)(s+3))/(s^3(s-1)) is (ks^3+6ks^2+11ks+6k)/(s^4-s^3)

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

expand

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

\frac{k s ^{3} + 6 k s ^{2} + 11 k s + 6 k}{s ^{4} - s ^{3}}

Solution steps

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

Expand

s^{3} (s - 1) : s^{4} - s^{3}

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

Expand

k (s + 1) (s + 2) (s + 3) : k s^{3} + 6 k s^{2} + 11 k s + 6 k

= \frac{k s ^{3} + 6 k s ^{2} + 11 k s + 6 k}{s ^{4} - s ^{3}}

(x - 3) (x + 2) (x - \frac{2}{3}) (x + 1)

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

(2 x y^{2} + 2 y) + (2 x^{2} y + 2 x) y^{'} (x)

(vx + x x^{2} - v^{2}) d x - x (v d x + x d v = 0)

(2 + x - 1) (2 + x - 1)

What is expand (k(s+1)(s+2)(s+3))/(s^3(s-1)) ?
The solution to expand (k(s+1)(s+2)(s+3))/(s^3(s-1)) is (ks^3+6ks^2+11ks+6k)/(s^4-s^3)