What is (k(s+1.5))/(s(s+1)(s+10)+1.5k) ?

The solution to (k(s+1.5))/(s(s+1)(s+10)+1.5k) is (k(s+1.5))/(s^3+11s^2+10s+1.5k)

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simplify (k(s+1.5))/(s(s+1)(s+10)+1.5k)

simplify

\frac{k ( s + 1.5 )}{s ( s + 1 ) ( s + 10 ) + 1.5 k}

\frac{k ( s + 1.5 )}{s ^{3} + 11 s ^{2} + 10 s + 1.5 k}

Solution steps

\frac{k ( s + 1.5 )}{s ( s + 1 ) ( s + 10 ) + 1.5 k}

Apply FOIL method

(s + 1) (s + 10) : s^{2} + 11 s + 10

= \frac{k ( s + 1.5 )}{s ( s ^{2} + 11 s + 10 ) + 1.5 k}

Apply the distributive law:

m (a + b + c) = ma + mb + m c

s (s^{2} + 11 s + 10) = s s^{2} + s \cdot 11 s + s \cdot 10

= \frac{k ( s + 1.5 )}{s s ^{2} + s \cdot 11 s + s \cdot 10 + 1.5 k}

Simplify

s s^{2} + s \cdot 11 s + s \cdot 10 : s^{3} + 11 s^{2} + 10 s

= \frac{k ( s + 1.5 )}{s ^{3} + 11 s ^{2} + 10 s + 1.5 k}

(x + i y - a - bi)^{2}

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

(1 + sin^{3} (t)) (3 sin^{2} (t) cos (t))

\frac{sin ^{2} ( ( x + 2 ) ( x - 2 ) )}{( x + 2 ) ( x - 2 )}

(x^{2} + 1) x

What is (k(s+1.5))/(s(s+1)(s+10)+1.5k) ?
The solution to (k(s+1.5))/(s(s+1)(s+10)+1.5k) is (k(s+1.5))/(s^3+11s^2+10s+1.5k)