Question

Rationalise the denominator of $\frac{1}{\sqrt{3}-\sqrt{2}-1}$

Answer 1

$\frac{1}{\sqrt{3}-(\sqrt{2}+1)}=\frac{\sqrt{3}+\sqrt{2}+1}{3-(\sqrt{2}+1{)}^2}=\frac{\sqrt{3}+\sqrt{2}+1}{3-2-1-2\sqrt{2}}=-\frac{\sqrt{3}+\sqrt{2}+1}{2\sqrt{2}}$