Square root (3)/(square root3 +square root2)

I was thinking that both square roots of 3 would cross out and leave square root 2

No - as with all fractions, if you divide the numerator by something, you have to divide the denominator by the same thing. In this case you divided the numerator by sqrt(3) leaving 1, and the denominator also by sqrt(3) leaving 1 +sqrt(2)/sqrt(3)

That would only work if the denominator was sqr(3) * sqr(2). With addition, you would need to factor a sqr(3) out of both parts. Can't quite remember how to solve this one, but I know you can't just cancel them.
Sorry :(