Question

Solve the equation $2\tan h^{-1}\left(\frac{x-2}{x+1}\right)=\ln 2$

Answer 1

$\Rightarrow \frac{x-2}{x+1}=tanh\left(\frac{1}{2}ln2\right)$

$\Rightarrow \frac{x-2}{x+1}=\frac{e^{2\times 1/2\times ln2}-1}{e^{2\times 1/2\times ln2}+1}$

$\Rightarrow \frac{x-2}{x+1}=1/3$

$\Rightarrow x=7/2=3.5$