Can anyone explain to me what happened here?
I understand that the 2 on the bottom is cause the denominator has to be the same, but I don't understand what happened on top.
Hello.
$\displaystyle \sqrt{2} - 2 \sqrt{2} =1* \sqrt{2} - 2* \sqrt{2} = -1 \sqrt{2}$. because
$\displaystyle 1* \sqrt{2} - 2* \sqrt{2} = (1-2)*\sqrt{2} = (-1)*\sqrt{2}$
After that you can add the remaining '2' to $\displaystyle (-1)*\sqrt{2}$, because all these terms have the same denominator!
This leads to -$\displaystyle 1*\sqrt{2}+2 = -\sqrt{2}+2$ on the top
Yours
Rapha