$$\eqalign{
& {{2\sqrt x - 1} \over {\left( {1 - \sqrt x } \right)\left( {1 - \sqrt x + x} \right)}}:{{x - 1 + \sqrt x } \over {1 - \sqrt x }} \cr
& = {{2\sqrt x - 1} \over {\left( {1 - \sqrt x } \right)\left( {1 - \sqrt x + x} \right)}}.{{1 - \sqrt x } \over {x - 1 + \sqrt x }} \cr
& = {{2\sqrt x - 1} \over {\left( {x - \sqrt x + 1} \right)\left( {x + \sqrt x - 1} \right)}} \cr
& = {{2\sqrt x - 1} \over {{x^2} - {{\left( {\sqrt x - 1} \right)}^2}}} \cr} $$