`D = (1; +infty)`
`log_{\sqrt{2}} (x - 1) +`$log_{\dfrac{1}{2}} (x + 1) = 1$
`->` $log_{2^{\dfrac{1}{2}}} (x - 1) + log_{2^{-1}} (x + 1) = 1$
`-> 2log_{2} (x - 1) - log_{2} (x + 1) = 1`
`-> log_{2} (x - 1)^{2} - log_{2} (x + 1) = 1`
`-> log_{2} (((x - 1)^2)/(x + 1)) = 1`
`-> ((x - 1)^2)/(x + 1) = 2^1 = 2`
`-> x^2 - 2x + 1 = 2x + 2`
`-> x^2 - 4x - 1 = 0`
`->` \(\left[ \begin{array}{l}x = \dfrac{5} + 2 \\x = 2 - \sqrt{5} (l)\end{array} \right.\)
`-> x = 2 + \sqrt{5}`
