What is the inverse of s/(s^2-6s-7) ?

The inverse of s/(s^2-6s-7) is (6s+1+sqrt(64s^2+12s+1))/(2s),(6s+1-sqrt(64s^2+12s+1))/(2s)

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inverse of s/(s^2-6s-7)

inverse

\frac{s}{s ^{2} - 6 s - 7}

\frac{6 s + 1 + 64 s ^{2} + 12 s + 1}{2 s}, \frac{6 s + 1 - 64 s ^{2} + 12 s + 1}{2 s}

Solution steps

y = \frac{s}{s ^{2} - 6 s - 7}

Replace

s

with

y

s = \frac{y}{y ^{2} - 6 y - 7}

Solve for

y, s = \frac{y}{y ^{2} - 6 y - 7}

\frac{6 s + 1 + 64 s ^{2} + 12 s + 1}{2 s}, \frac{6 s + 1 - 64 s ^{2} + 12 s + 1}{2 s}

What is the inverse of s/(s^2-6s-7) ?
The inverse of s/(s^2-6s-7) is (6s+1+sqrt(64s^2+12s+1))/(2s),(6s+1-sqrt(64s^2+12s+1))/(2s)