Expressing in rationals I have this question to express it in a specific form

Express $\dfrac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$ in the form $a \sqrt{2} + b \sqrt{3} + c \sqrt{7} + d \sqrt{42}$, for some rationals $a,b,c$ and $d$.

So the solution that I have and am trying to understand is this

So what I don't understand is that why in the world is there a 2sqrt6 here where did it come from?

$(\sqrt{2}+\sqrt{3}+\sqrt{7})(\sqrt{2}+\sqrt{3}-\sqrt{7})$
$=(\sqrt{2}+\sqrt{3})^2-(\sqrt{7})^2$
$=(\sqrt{2})^2+(\sqrt{3})^2+2\sqrt{2}\sqrt{3}-(\sqrt{7})^2$
$=2+3+2\sqrt{6}-7$
$=2\sqrt 6-2$
