Multiply the numerator and the denominator by the same number and you can change it to whatever number you need.
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The same way as with a positive denominator. The difference is, you change the sign of the numerator.
To eliminate the radical in the denominator.
because of mathematical equivalence: it doesn't change the result
Yes. The original denominator and its conjugate will form the factors of a Difference of Two Squares (DOTS) and that will rationalise the denominator but only if the radicals are SQUARE roots.
1 is the only common denominator.