Lösung 3.1:6d
Aus Online Mathematik Brückenkurs 1
The problem with this expression is that the denominator contains three roots and so there is no simple way to get rid of all root signs at once; rather, we need to work step by step. In the first step, we view the numerator as \displaystyle (\sqrt{2}+\sqrt{3})+\sqrt{6} and multiply the top and bottom of the fraction by the conjugate-like expression \displaystyle (\sqrt{2}+\sqrt{3})-\sqrt{6}\,. Then, at least \displaystyle \sqrt{6} will be squared away using the formula for the difference of two squares
We expand the remaining quadratic, \displaystyle (\sqrt{2}+\sqrt{3})^{2}, using the formula for the difference of two squares,
This expression has only a root sign in the denominator and we can then complete the calculation by multiplying top and bottom by the conjugate \displaystyle 2\sqrt{6}+1,
