How can this sinh curve be massaged?

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Sorry I'm new here so I don't know how to use the math symbols yet but I would really appreciate some help with something I'm stuck on.

How can this equation:

$$ ()= \sinh(\sinh^{-1}(_0)−\rho \log) $$

Be reformulated as:

$$ y(x)=\frac{x}{2}\left(\sqrt{1+y_0^2}\left(x^{-\rho}-x^\rho\right)+y_0\left(x^{-\rho}+x^\rho\right)\right) $$

It is a step that wasn't explained by user26872 in his reponse to the following question: Name that curve!

Thank you!