Our goal in simplifying expressions with radicals is to ensure that there are no roots in the denominator. It is OK to have radicals in the numerator as long as we simplify as much as possible. To get the sum or difference of two radicals out of the denominator, we need to multiply top and bottom of the fraction by the conjugate of the bottom. Mathematically, this is just multiplying by one, so we're not changing the value of the fraction, but if done correctly, the radical terms in the denominator will cancel out.
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