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Help me understand the part after the second '=', what on earth is going on in the numerator. The denominator and other parts I understand.

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numerator is basically expansion of $(a-b)(a-b)=a^2-2ab+b^2$ –  Mufasa Aug 9 at 19:41

3 Answers 3

$$(\sqrt{6}-\sqrt{2})(\sqrt{6}-\sqrt{2})=\sqrt{6}(\sqrt{6}-\sqrt{2})-\sqrt{2}(\sqrt{6}-\sqrt{2})=6-2\sqrt{6}\sqrt{2}+2$$

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If you are asking how they get

$$(\sqrt6-\sqrt2)(\sqrt6-\sqrt2)=6-2\sqrt6\sqrt2+2$$

they are applying the standard algebra formula

$$(a-b)^2=a^2-2ab+b^2$$ with $a=\sqrt6$ and $b=\sqrt2$.

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At the numerator, the writer expanded $(\sqrt 6 - \sqrt 2)^2$.

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