What is (1/s)/(1+K a/(bs+c)) ?

The solution to (1/s)/(1+K a/(bs+c)) is (bs+c)/(s(bs+c+Ka))

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simplify (1/s)/(1+K a/(bs+c))

simplify

\frac{\frac{1}{s}}{1 + K \frac{a}{b s + c}}

\frac{b s + c}{s ( b s + c + K a )}

Solution steps

\frac{\frac{1}{s}}{1 + K \frac{a}{b s + c}}

Apply the fraction rule:

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

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

Simplify

s (1 + K \frac{a}{b s + c}) : \frac{s ( b s + c + K a )}{b s + c}

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

Apply the fraction rule:

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

= \frac{b s + c}{s ( b s + c + K a )}

28 + 9

+ \frac{π}{\frac{2}{3}}

42 - 3

45 + 9

\frac{6}{8} - \frac{6}{3}

What is (1/s)/(1+K a/(bs+c)) ?
The solution to (1/s)/(1+K a/(bs+c)) is (bs+c)/(s(bs+c+Ka))