How can you write the expression below with a rationalized denominator sqrt3-sqrt6/sqrt3+sqrt6

Rewriting the given expression by rationalizing the denominator we proceed as follows:

[√3-√6]/[√3+√6]

to rationalize the denominator we multiply the numerator and the denominator by the conjugate. Thus we shall have:

[√3-√6]/[√3+√6]*[√3-√6]/[√3-√6]

={√3 (√3-√6) - √6 (√3-√6) }/{√3 (√3+√6) - √6 (√3+√6) }

=[3-√3√6-√3√6+6]/[3+√3√6-√3√6-6]

simplifying the above we obtain:

[3-2√18+6]/[3-6]

=[3+6-6√2] / (-3)

=[9-6√2] / (-3)

=2√2-3

Answer: 2√2-3