Equation arrangement. How to arrange $x=\frac{1}{2} \ln({1+\frac{10}{x}})$ to $x=\frac{10}{e^{2x}-1}$ ?
Can anyone give me step by step explanation? Thanks in advance.

$x=\frac{1}{2} \ln(1+ \frac{10}{x}) \implies 2x= \ln(1+ \frac{10}{x}) \implies
e^{2x} = 1+ \frac{10}{x} \implies e^{2x} - 1 =\frac{10}{x} \implies x= \frac{10}{ e^{2x} - 1}
$
