What is 1+k/(s^2+(5+k)s+0.5) ?

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

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simplify 1+k/(s^2+(5+k)s+0.5)

simplify

1 + \frac{k}{s ^{2} + ( 5 + k ) s + 0.5}

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

Solution steps

1 + \frac{k}{s ^{2} + ( 5 + k ) s + 0.5}

Apply the fraction rule:

1 + \frac{b}{c} = \frac{c + b}{c}

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

Apply rule:

(a) = a

(s^{2} + (5 + k) s + 0.5) = s^{2} + (5 + k) s + 0.5

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

Simplify

s^{2} + (5 + k) s + 0.5 + k : s^{2} + 5 s + k s + 0.5 + k

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

\frac{3 ( 3 x - 2 )}{x - 4}

(2 - 2) (2 + 2)

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

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

\frac{3 x}{2} + \frac{x}{2}

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