[latex]frac{x+sqrt{2}}{sqrt{3}+1} < frac{x-sqrt{3}}{sqrt{2}+1}[/latex] [latex]frac{x+sqrt{2}}{sqrt{3}+1} - frac{x-sqrt{3}}{sqrt{2}+1} < 0[/latex] [latex]frac{(x+sqrt{2})(sqrt{2}+1)}{(sqrt{3}+1)(sqrt{2}+1)} - frac{(x-sqrt{3})(sqrt{3}+1)}{(sqrt{3}+1)(sqrt{2}+1)} < 0[/latex] [latex]frac{(x+sqrt{2})(sqrt{2}+1)-(x-sqrt{3})(sqrt{3}+1)}{(sqrt{3}+1)(sqrt{2}+1)} <0 / cdot (sqrt{3}+1)(sqrt{2}+1)[/latex] [latex](x+sqrt{2})(sqrt{2}+1)-(x-sqrt{3})(sqrt{3}+1) < 0[/latex] [latex]xsqrt{2} + x + 2 +sqrt{2} - (xsqrt{3}+x-3-sqrt{3}) < 0[/latex] [latex]xsqrt{2} + x + 2 +sqrt{2} - xsqrt{3}-x+3+sqrt{3}< 0[/latex] [latex]xsqrt{2} - xsqrt{3}+5+sqrt{3}+sqrt{2} < 0[/latex] [latex]xsqrt{2} - xsqrt{3}< - 5-sqrt{3}-sqrt{2}[/latex] [latex]x(sqrt{2} - sqrt{3}) < - (5+sqrt{3}+sqrt{2}) /:sqrt{2} - sqrt{3})[/latex] [latex]x > frac{- (5+sqrt{3}+sqrt{2})}{sqrt{2} - sqrt{3}}[/latex] [latex]x > frac{- (5+sqrt{3}+sqrt{2})(sqrt{2} + sqrt{3})}{(sqrt{2} - sqrt{3})(sqrt{2} + sqrt{3})}[/latex] [latex]x > frac{- (5+sqrt{3}+sqrt{2})(sqrt{2} + sqrt{3})}{2-3}[/latex] [latex]x > frac{- (5+sqrt{3}+sqrt{2})(sqrt{2} + sqrt{3})}{-1}[/latex] [latex]x > (5+sqrt{3}+sqrt{2})(sqrt{2} + sqrt{3})[/latex] [latex]x > 5sqrt{2} + 5sqrt{3} + sqrt{6} +3 + 2 + sqrt{6}[/latex] [latex]x > 5 + 2sqrt{6}+ 5sqrt{3} + 5sqrt{2} approx 25,63[/latex]
