What is the simplest form of expression?
sqrt 3 - sqrt 6
over
sqrt 3 + sqrt 6

(√3-√6) / (√3+√6)
We have to multiply the denominator and numerator by the conjugate of the denominator.
the conjugate of the denominator is :(√3-√6)

Therefore:

(√3-√6) / (√3+√6) =[(√3-√6)(√3-√6)]  /  [(√3+√6)(√3-√6)]
=(√3-√6)² / (3-6)
=[3-2(√3)(√6)+6] / -3
=(9-2√18) / -3
=(-9+6√2) /3
=-3+2√2

(√3-√6) / (√3+√6)= -3+2√2