The value of 1 + tanh x 1 - tanh x is

Putting the value of $\tan \text{h}x$ in terms of $e^x$ we get,

$\frac{1+\tanh x}{1-\tanh x}$

$=\frac{1+\frac{e^x-e^{-x}}{e^x+e^{-x}}}{1-\frac{e^x-e^{-x}}{e^x+e^{-x}}}$

$=\frac{e^x+e^{-x}+e^x-e^{-x}}{e^x+e^{-x}-e^x+e^{-x}}$

$=\frac{2e^x}{2e^{-x}}$

$=e^{2x}$ .