\frac{\sqrt{x+2}-\sqrt{3x-2}}{\sqrt{4x+1}-\sqrt{5x-1}}=\frac{\displaystyle\phantom{x}\frac{4-2x}{\sqrt{x+2}+\sqrt{3x-2}}\phantom{x}}{\displaystyle\frac{2-x}{\sqrt{4x+1}+\sqrt{5x-1}}}=2\,\frac{\sqrt{4x+1}+\sqrt{5x-1}}{\sqrt{x+2}+\sqrt{3x-2}}.