\(\dfrac{\sqrt 2+\sqrt3+\sqrt 6+\sqrt 8+4}{\sqrt2+\sqrt 3+\sqrt 4}\)
\(=\dfrac{\sqrt 2+\sqrt3+2+\sqrt 6+\sqrt 8+2}{\sqrt2+\sqrt 3+\sqrt 4}\)
\(=\dfrac{\sqrt 2+\sqrt3+\sqrt 4+\sqrt 6+\sqrt 8+\sqrt 4}{\sqrt2+\sqrt 3+\sqrt 4}\)
\(=1+\dfrac{\sqrt 2(\sqrt3+\sqrt4+\sqrt2)}{\sqrt2+\sqrt 3+\sqrt 4}\)
\(=1+1\)
\(=2\)