What is the inverse of (1-2s)/(s^2+4s+5) ?

The inverse of (1-2s)/(s^2+4s+5) is (-2s-1+sqrt(-s^2+5s+1))/s ,-(2s+sqrt(-s^2+5s+1)+1)/s

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inverse of (1-2s)/(s^2+4s+5)

inverse

\frac{1 - 2 s}{s ^{2} + 4 s + 5}

\frac{- 2 s - 1 + - s ^{2} + 5 s + 1}{s}, - \frac{2 s + - s ^{2} + 5 s + 1 + 1}{s}

Solution steps

y = \frac{1 - 2 s}{s ^{2} + 4 s + 5}

Replace

s

with

y

s = \frac{1 - 2 y}{y ^{2} + 4 y + 5}

Solve for

y, s = \frac{1 - 2 y}{y ^{2} + 4 y + 5}

\frac{- 2 s - 1 + - s ^{2} + 5 s + 1}{s}, - \frac{2 s + - s ^{2} + 5 s + 1 + 1}{s}

What is the inverse of (1-2s)/(s^2+4s+5) ?
The inverse of (1-2s)/(s^2+4s+5) is (-2s-1+sqrt(-s^2+5s+1))/s ,-(2s+sqrt(-s^2+5s+1)+1)/s