Answer
$-2\ln \left( x-1\right) $
Work Step by Step
We use the rules of logarithms to obtain:
$\ln \left( \dfrac {x}{x-1}\right) +\ln \left( \dfrac {x+1}{x}\right) -\ln \left( x^{2}-1\right) =\ln \left( \dfrac {x}{x-1}\times \dfrac {x+1}{x}\times \dfrac {1}{x^{2}-1}\right) =\ln \left( \dfrac {1}{x-1}\right) ^{2}=-2\ln \left( x-1\right) $
