Rationalising surd/simplifying denominator

Hello

I have been struggling terribly with a surd problem to the point that it's beginning to hurt }:-/

I have: √3

√2(√6-√3)

The answer is given as :

(2+√2)

2

I want to multiply the denominator by itself to clear the surds, but end up with a way too complicated answer.

I realise that

(√6-√3)(√6+√3) would rationalise part of the problem, but the √2 is really giving me a hard time...Using logic I feel I want to multiply by √2(√6+√3) but can't get anywhere near the answer if I do.

Cold someone shed some light for me please ?

Thank you!

Apologies for formatting, the question and answer are fractions of course*