Question

\(\dfrac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}-\dfrac{10}{1+\sqrt{6}}\)

Answer 1

\(=\dfrac{\left(3\sqrt{2}-2\sqrt{3}\right)\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}-\dfrac{10\left(\sqrt{6}-1\right)}{\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}\)
\(=\dfrac{3\sqrt{6}+6-6-2\sqrt{6}}{3-2}-\dfrac{10\left(\sqrt{6}-1\right)}{6-1}\)
\(=\sqrt{6}-\dfrac{10\left(\sqrt{6}-1\right)}{5}=\sqrt{6}-2\left(\sqrt{6}-1\right)=\sqrt{6}-2\sqrt{6}+2=2-\sqrt{6}\)