y = (e^6x + e^−6x)/ (e^6x − e^−6x)

$${\mathtt{y}} = {\frac{\left({{\mathtt{e}}}^{\left({\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{\left({{\mathtt{e}}}^{\left({\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}\right)}}\right)}{\left({{\mathtt{e}}}^{\left({\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{\left({{\mathtt{e}}}^{\left({\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}\right)}}\right)}}$$

$${\mathtt{y}} = {\frac{\left({\frac{\left({{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{{{\mathtt{e}}}^{\left({\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}}}\right)}{\left({\frac{\left({{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{{\mathtt{e}}}^{\left({\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}}}\right)}}$$

$${\mathtt{y}} = {\frac{\left({{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{\left({{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}$$

$${\mathtt{y}} = {\frac{\left({{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{\left({{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}$$

$${\mathtt{y}} = {\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{\left({{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}$$

$${\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{1}} = {\frac{{\mathtt{2}}}{\left({{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}$$

$$\left(\left({\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{1}}\right){\mathtt{\,\times\,}}\left({{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{1}}\right)\right) = {\mathtt{2}}$$

$${{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}{\mathtt{\,-\,}}{\mathtt{1}} = {\frac{{\mathtt{2}}}{\left({\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}$$

$${{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)} = {\frac{{\mathtt{2}}}{\left({\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}$$

$${{\mathtt{e}}}^{\left({\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)} = {\frac{\left({\mathtt{y}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{\left({\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}$$

$${\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}} = {ln}{\left({\mathtt{y}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}$$

$${\mathtt{x}} = {\frac{\left({ln}{\left({\mathtt{y}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}\right)}{{\mathtt{12}}}}$$

In the second-to-the-last line, shouldn't the times sign be a minus sign?

That is:  12x  =  ln(y + 1)  -  ln(y - 1)

                x  =  [ ln(y + 1)  -  ln(y - 1) ] / 12

Yes, it should be. I made an arithmetic error.