What is expand (K(s+a))/(s+1)*1/(s(s+2)(s+3)) ?

The solution to expand (K(s+a))/(s+1)*1/(s(s+2)(s+3)) is (Ks+aK)/(s^4+6s^3+11s^2+6s)

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expand (K(s+a))/(s+1)*1/(s(s+2)(s+3))

expand

\frac{K ( s + a )}{s + 1} \cdot \frac{1}{s ( s + 2 ) ( s + 3 )}

\frac{Ks + a K}{s ^{4} + 6 s ^{3} + 11 s ^{2} + 6 s}

Solution steps

\frac{K ( s + a )}{s + 1} \cdot \frac{1}{s ( s + 2 ) ( s + 3 )}

\frac{K ( s + a )}{s + 1} = \frac{Ks + a K}{s + 1}

= \frac{Ks + a K}{s + 1} \cdot \frac{1}{s ( s + 2 ) ( s + 3 )}

\frac{1}{s ( s + 2 ) ( s + 3 )} = \frac{1}{s ^{3} + 5 s ^{2} + 6 s}

= \frac{Ks + a K}{s + 1} \cdot \frac{1}{s ^{3} + 5 s ^{2} + 6 s}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( Ks + a K ) \cdot 1}{( s + 1 ) ( s ^{3} + 5 s ^{2} + 6 s )}

(Ks + a K) \cdot 1 = Ks + a K

= \frac{Ks + a K}{( s + 1 ) ( s ^{3} + 5 s ^{2} + 6 s )}

Expand

(s + 1) (s^{3} + 5 s^{2} + 6 s) : s^{4} + 6 s^{3} + 11 s^{2} + 6 s

= \frac{Ks + a K}{s ^{4} + 6 s ^{3} + 11 s ^{2} + 6 s}

\frac{6 ( 2 N ^{2} + 3 N + 1 )}{N ^{2}}

4 \cdot (a \cdot (2 + 2^{t} + 3^{t}))

(1 + 3 j) (1 - 3 j)

\frac{( x - 1 ) ( x - 2.5 )}{( x - 3 )} - 1

(ni + 2)^{2}

What is expand (K(s+a))/(s+1)*1/(s(s+2)(s+3)) ?
The solution to expand (K(s+a))/(s+1)*1/(s(s+2)(s+3)) is (Ks+aK)/(s^4+6s^3+11s^2+6s)