I tried to post earlier but apparently did not press the correct button.
I did finally notice that e-2x(K+P0(e2x -1))would equal 0+P0*1 -0.
This would equal KP0 in the numerator and P0 in denominator.
So the answer is K

Thanks for everyone's help. I will check into the concepts of the other posts as well.
What is the technique of multiplying that way called? It is almost like rationalizing the numerator?