Just for fun

$\eqalign{ & \left( {x - 2} \right)^2 - 1 = \frac{2} {{\left( {x - 2} \right)^2 }} \cr & \left( {\left( {x - 2} \right)^2 } \right)^2 - \left( {x - 2} \right)^2 = 2 \cr & \left( {\left( {x - 2} \right)^2 } \right)^2 - \left( {x - 2} \right)^2 - 2 = 0 \cr & \left( {\left( {x - 2} \right)^2 - 2} \right)\left( {\left( {x - 2} \right)^2 + 1} \right) = 0 \cr & \left( {x - 2} \right)^2 - 2 = 0 \vee \left( {x - 2} \right)^2 + 1 = 0 \cr & \left( {x - 2} \right)^2 = 2 \vee \left( {x - 2} \right)^2 = - 1\,\,(k.n.) \cr & x - 2 = - \sqrt 2 \vee x - 2 = \sqrt 2 \cr & x = 2 - \sqrt 2 \vee x = 2 + \sqrt 2 \cr}$