What is the inverse of (s^2+6s+8)/(s^2+2) ?

The inverse of (s^2+6s+8)/(s^2+2) is (-3+sqrt(-2s^2+10s+1))/(1-s),-(sqrt(-2s^2+10s+1)+3)/(-s+1)

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inverse of (s^2+6s+8)/(s^2+2)

inverse

\frac{s ^{2} + 6 s + 8}{s ^{2} + 2}

\frac{- 3 + - 2 s ^{2} + 10 s + 1}{1 - s}, - \frac{- 2 s ^{2} + 10 s + 1 + 3}{- s + 1}

Solution steps

y = \frac{s ^{2} + 6 s + 8}{s ^{2} + 2}

Replace

s

with

y

s = \frac{y ^{2} + 6 y + 8}{y ^{2} + 2}

Solve for

y, s = \frac{y ^{2} + 6 y + 8}{y ^{2} + 2}

\frac{- 3 + - 2 s ^{2} + 10 s + 1}{1 - s}, - \frac{- 2 s ^{2} + 10 s + 1 + 3}{- s + 1}

What is the inverse of (s^2+6s+8)/(s^2+2) ?
The inverse of (s^2+6s+8)/(s^2+2) is (-3+sqrt(-2s^2+10s+1))/(1-s),-(sqrt(-2s^2+10s+1)+3)/(-s+1)