What is the inverse of (s-5)/((s+3)(s-2)) ?

The inverse of (s-5)/((s+3)(s-2)) is (-s+1+sqrt(25s^2-22s+1))/(2s),(-s+1-sqrt(25s^2-22s+1))/(2s)

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inverse of (s-5)/((s+3)(s-2))

inverse

\frac{s - 5}{( s + 3 ) ( s - 2 )}

\frac{- s + 1 + 25 s ^{2} - 22 s + 1}{2 s}, \frac{- s + 1 - 25 s ^{2} - 22 s + 1}{2 s}

Solution steps

y = \frac{s - 5}{( s + 3 ) ( s - 2 )}

Replace

s

with

y

s = \frac{y - 5}{( y + 3 ) ( y - 2 )}

Solve for

y, s = \frac{y - 5}{( y + 3 ) ( y - 2 )}

\frac{- s + 1 + 25 s ^{2} - 22 s + 1}{2 s}, \frac{- s + 1 - 25 s ^{2} - 22 s + 1}{2 s}

f (x) = - 6 x^{5} + 8

y = 2^{x - 3} - 5

f (x) = \frac{5 y + 1}{2 - 5 y}

arccosh (x)

f (x) = \frac{6 x + 1}{4 x - 6}

What is the inverse of (s-5)/((s+3)(s-2)) ?
The inverse of (s-5)/((s+3)(s-2)) is (-s+1+sqrt(25s^2-22s+1))/(2s),(-s+1-sqrt(25s^2-22s+1))/(2s)