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

The solution to (k(s+0.5))/((s+2)^2(s+1)+k(s+0.5)) is (k(s+0.5))/(s^3+5s^2+8s+4+ks+0.5k)

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

simplify

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

\frac{k ( s + 0.5 )}{s ^{3} + 5 s ^{2} + 8 s + 4 + k s + 0.5 k}

Solution steps

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

Expand

(s + 2)^{2} (s + 1) : s^{3} + 5 s^{2} + 8 s + 4

= \frac{k ( s + 0.5 )}{s ^{3} + 5 s ^{2} + 8 s + 4 + k ( s + 0.5 )}

Expand

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

= \frac{k ( s + 0.5 )}{s ^{3} + 5 s ^{2} + 8 s + 4 + k s + 0.5 k}

3 sin (θ^{2}) - (1 + sin (θ))^{2} d θ

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

\frac{( 10 x ^{2} + y ^{2} + 5 x y ) x y}{5}

\frac{2 + s}{( 100 + s ) ^{2}}

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

What is (k(s+0.5))/((s+2)^2(s+1)+k(s+0.5)) ?
The solution to (k(s+0.5))/((s+2)^2(s+1)+k(s+0.5)) is (k(s+0.5))/(s^3+5s^2+8s+4+ks+0.5k)