$$\eqalign{
& 3)\,\,{{\sqrt x - 1} \over {\sqrt x + 1}} + {{2x - \sqrt x - 1} \over {x - \sqrt x + 1}} - {{3x\sqrt x - 2x + \sqrt x - 3} \over {x\sqrt x + 1}}\,\,\left( {x \ge 0} \right) \cr
& = {{\left( {\sqrt x - 1} \right)\left( {x - \sqrt x + 1} \right) + \left( {\sqrt x + 1} \right)\left( {2x - \sqrt x - 1} \right) - \left( {3x\sqrt x - 2x + \sqrt x - 3} \right)} \over {\left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}} \cr
& = {{x\sqrt x - x + \sqrt x - x + \sqrt x - 1 + 2x\sqrt x - x - \sqrt x + 2x - \sqrt x - 1 - 3x\sqrt x + 2x - \sqrt x + 3} \over {\left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}} \cr
& = {{x - \sqrt x + 1} \over {\left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}} = {1 \over {\sqrt x + 1}} \cr
& 6)\,\,{{\sqrt x - 1} \over {\sqrt x + 1}} - {{\sqrt x + 3} \over {\sqrt x - 2}} - {{x + 5} \over {x - \sqrt x - 2}}\,\,\left( {x \ge 0;\,\,x \ne 4} \right) \cr
& = {{\left( {\sqrt x - 1} \right)\left( {\sqrt x - 2} \right) - \left( {\sqrt x + 3} \right)\left( {\sqrt x + 1} \right) - \left( {x + 5} \right)} \over {\left( {\sqrt x + 1} \right)\left( {\sqrt x - 2} \right)}} \cr
& = {{x - 3\sqrt x + 2 - \left( {x + 4\sqrt x + 3} \right) - x - 5} \over {\left( {\sqrt x + 1} \right)\left( {\sqrt x - 2} \right)}} \cr
& = {{x - 3\sqrt x + 2 - x - 4\sqrt x - 3 - x - 5} \over {\left( {\sqrt x + 1} \right)\left( {\sqrt x - 2} \right)}} \cr
& = {{ - x - 7\sqrt x - 6} \over {\left( {\sqrt x + 1} \right)\left( {\sqrt x - 2} \right)}} \cr
& = {{ - \left( {\sqrt x + 1} \right)\left( {\sqrt x + 6} \right)} \over {\left( {\sqrt x + 1} \right)\left( {\sqrt x - 2} \right)}} = - {{\sqrt x + 6} \over {\sqrt x - 2}} \cr
& 11)\,\,{{\sqrt x - 3} \over {2 - \sqrt x }} + {{\sqrt x - 2} \over {3 + \sqrt x }} - {{9 - x} \over {x + \sqrt x - 6}}\,\,\left( {x \ge 0;\,\,x \ne 4} \right) \cr
& = {{\left( {3 - \sqrt x } \right)\left( {3 + \sqrt x } \right) + {{\left( {\sqrt x - 2} \right)}^2} - \left( {9 - x} \right)} \over {\left( {\sqrt x - 2} \right)\left( {\sqrt x + 3} \right)}} \cr
& = {{9 - x + x - 4\sqrt x + 4 - 9 + x} \over {\left( {\sqrt x - 2} \right)\left( {\sqrt x + 3} \right)}} \cr
& = {{x - 4\sqrt x + 4} \over {\left( {\sqrt x - 2} \right)\left( {\sqrt x + 3} \right)}} \cr
& = {{{{\left( {\sqrt x - 2} \right)}^2}} \over {\left( {\sqrt x - 2} \right)\left( {\sqrt x + 3} \right)}} = {{\sqrt x - 2} \over {\sqrt x + 3}} \cr
& 17)\,\,{{ - 31 + 8\sqrt x - x} \over {x - 8\sqrt x + 15}} - {{\sqrt x + 5} \over {\sqrt x - 3}} - {{3\sqrt x - 1} \over {5 - \sqrt x }}\,\,\left( {x \ge 0;\,\,x \ne 9;\,\,x \ne 25} \right) \cr
& = {{ - 31 + 8\sqrt x - x - \left( {\sqrt x + 5} \right)\left( {\sqrt x - 5} \right) + \left( {3\sqrt x - 1} \right)\left( {\sqrt x - 3} \right)} \over {\left( {\sqrt x - 5} \right)\left( {\sqrt x - 3} \right)}} \cr
& = {{ - 31 + 8\sqrt x - x - \left( {x - 25} \right) + 3x - 9\sqrt x - \sqrt x + 3} \over {\left( {\sqrt x - 5} \right)\left( {\sqrt x - 3} \right)}} \cr
& = {{ - 31 + 8\sqrt x - x - x + 25 + 3x - 9\sqrt x - \sqrt x + 3} \over {\left( {\sqrt x - 5} \right)\left( {\sqrt x - 3} \right)}} \cr
& = {{x - 2\sqrt x - 3} \over {\left( {\sqrt x - 5} \right)\left( {\sqrt x - 3} \right)}} \cr
& = {{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 1} \right)} \over {\left( {\sqrt x - 5} \right)\left( {\sqrt x - 3} \right)}} = {{\sqrt x + 1} \over {\sqrt x - 5}} \cr} $$
