5: The expression in the numerator is of the type ∞ − ∞. The leading term under the root is n⁴, so when the root is taken into account, the first term behaves like n² when n goes to infinity, that is, it is of the same order as the second term "-n²". In intuitive calculations the leading terms cancel out

so we know that factoring out would not help.

Instead the best bet seems to be getting rid of the square root algebraically, see the box "difference of roots".

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