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`4/[\sqrt3-\sqrt5]-4/[\sqrt3+\sqrt5]`
`=[4(\sqrt3+\sqrt5)]/[(\sqrt3+\sqrt5)(\sqrt3-\sqrt5)]-[4(\sqrt3-\sqrt5)]/[(\sqrt3+\sqrt5)(\sqrt3-\sqrt5)]`
`=[4(\sqrt3+\sqrt5)-4(\sqrt3-\sqrt5)]/[(\sqrt3)^2-(\sqrt5)^2]`
`=[4(\sqrt3+\sqrt5-\sqrt3+\sqrt5)]/[3-5]`
`=[8\sqrt5]/[-2]`
`= -4\sqrt5`