Solve the equation and check the solution Enter your answers

Solve the equation and check the solution. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) -3/s^2 + 3s - 4 + 9/s + 4 = 1/s - 1 Identify any extraneous values. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Solution

-3/(s² + 3s - 4) + 9/(s + 4) = 1/(s - 1)

==> -3/(s² + 4s - s - 4) + 9/(s + 4) = 1/(s - 1)

==> -3/[s(s + 4) - 1(s + 4)] + 9/(s + 4) = 1/(s - 1)

==> -3/[(s + 4)(s - 1)] + 9/(s + 4) = 1/(s - 1)

==> (- 3 + 9(s -1) )/[(s + 4)(s - 1)] = 1/(s- 1)

==> (- 3 + 9s -9 )/(s + 4) = 1

==> 9s - 12 = s + 4

==> 9s - s = 4 + 12

==> 8s = 16

==> s = 2

Hence solution is s = 2

An extraneous solution is solution of transformed equation that is not a solution of original equation. since it is not in the domain odf original equation

Here s = 2 is solution of transformed equation. it is in the domain of original equation

Hence extraneous solutions does not exist