What is (k(s+0.5))/((s+1)(s^2+2s)+k(s+0.5)) ?

The solution to (k(s+0.5))/((s+1)(s^2+2s)+k(s+0.5)) is (k(s+0.5))/(s^3+3s^2+2s+ks+0.5k)

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simplify (k(s+0.5))/((s+1)(s^2+2s)+k(s+0.5))

simplify

\frac{k ( s + 0.5 )}{( s + 1 ) ( s ^{2} + 2 s ) + k ( s + 0.5 )}

\frac{k ( s + 0.5 )}{s ^{3} + 3 s ^{2} + 2 s + k s + 0.5 k}

Solution steps

\frac{k ( s + 0.5 )}{( s + 1 ) ( s ^{2} + 2 s ) + k ( s + 0.5 )}

Expand

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

= \frac{k ( s + 0.5 )}{s ^{3} + 3 s ^{2} + 2 s + k ( s + 0.5 )}

Expand

k (s + 0.5) : k s + 0.5 k

= \frac{k ( s + 0.5 )}{s ^{3} + 3 s ^{2} + 2 s + k s + 0.5 k}

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

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

\frac{( x - 5 )}{( 1 - x ) ( x + 2 )}

\frac{( 7 x - 1 ) ( 5 x - 2 )}{( x - 2 )}

\frac{p ( 1 - p ) ( n - 1 )}{n}

What is (k(s+0.5))/((s+1)(s^2+2s)+k(s+0.5)) ?
The solution to (k(s+0.5))/((s+1)(s^2+2s)+k(s+0.5)) is (k(s+0.5))/(s^3+3s^2+2s+ks+0.5k)