`\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{1}{\sqrt{3}-\sqrt{2}}`
`=\frac{\sqrt{3}-\sqrt{2}}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}-\frac{\sqrt{3}+\sqrt{2}}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}`
`=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}^2-\sqrt{2}^2}-\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}^2-\sqrt{2}^2}`
`=\frac{\sqrt{3}-\sqrt{2}}{3-2}-\frac{\sqrt{3}+\sqrt{2}}{3-2}`
`=\frac{\sqrt{3}-\sqrt{2}}{1}-\frac{\sqrt{3}+\sqrt{2}}{1}`
`=(\sqrt{3}-\sqrt{2})-(\sqrt{3}+\sqrt{2})`
`=\sqrt{3}-\sqrt{2}-\sqrt{3}-\sqrt{2}`
`=-2\sqrt{2}`