Inverse laplace transform

Hello there.

I have tried to get the inverse laplace transform of the following expression:

e^(-x*√(s/α))/(s*(k/h*√(s/α)+1))

So the inversion is gonna be done with respect to "s", from the frequency domain to the time domain.

Collegaues at work says that this is the solution after simplifying when put in x=0 into the inverse transform

But Im not the procedure is and have tried to check this at litterature and also the internet without clear results.

Does some know how to do this? I have tried to calculate the residues but ending up with different value so Im not sure this is even the right answer.

Best regards