Simplify this division of square roots?
We will continue under the assumption that "simplifying" requires rationalizing the denominator.
First, we can remove fractions from the numerator and denominator by multiplying both by
Then, we rationalize the denominator by multiplying by the conjugate of the denominator, and taking advantage of the identity
We will make use of the fact that
But before we can do that, we need to add the fractions in the denominator to make one fraction.
Now rationalise the denominator: