What is the inverse of ((s+3))/((s+2)(s+1)) ?

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

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inverse of ((s+3))/((s+2)(s+1))

inverse

\frac{( s + 3 )}{( s + 2 ) ( s + 1 )}

\frac{- 3 s + 1 + s ^{2} + 6 s + 1}{2 s}, \frac{- 3 s + 1 - s ^{2} + 6 s + 1}{2 s}

Solution steps

y = \frac{s + 3}{( s + 2 ) ( s + 1 )}

Replace

s

with

y

s = \frac{y + 3}{( y + 2 ) ( y + 1 )}

Solve for

y, s = \frac{y + 3}{( y + 2 ) ( y + 1 )}

\frac{- 3 s + 1 + s ^{2} + 6 s + 1}{2 s}, \frac{- 3 s + 1 - s ^{2} + 6 s + 1}{2 s}

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