what steps are needed to rewrite this function?

Question

I have two functions. What steps are needed to rewrite Z1 to Z2? If possible at all?

$$ Z_{1}(t) = P - \frac{P\mu }{e^{\frac{P}{N}t} + \mu} $$ $$ Z_{2}(t)= \frac{-Pe^{\frac{P}{N}t}}{\mu+e^{\frac{P}{N}t}} $$

Answer 1

$Z_{1}(t) = P - \dfrac{P\mu }{e^{\frac{P}{N}t} + \mu}$

$Z_{2}(t)= \dfrac{-Pe^{\frac{P}{N}t}}{\mu+e^{\frac{P}{N}t}}$

$\implies \dfrac{Z_{2}(t)}{e^{\frac{P}{N}t}}= \dfrac{-P}{\mu+e^{\frac{P}{N}t}}$

$\therefore Z_{1}(t) = P +\mu\cdot \dfrac{Z_{2}(t)}{e^{\frac{P}{N}t}}$

$\implies Z_2(t) = \dfrac{(Z_1(t)-P)e^{\frac PN\cdot t}}{\mu} $