Answer: The answer is [tex]-3+\dfrac{2}{3}\sqrt{18}.[/tex]
Step-by-step explanation: The given expression is
[tex]E=\dfrac{\sqrt 3-\sqrt 6}{\sqrt 3+\sqrt 6}.[/tex]
we will be rationalising the given expression as follows:
[tex]E\\\\\\=\dfrac{\sqrt 3-\sqrt 6}{\sqrt 3+\sqrt 6}\\\\\\=\dfrac{(\sqrt 3-\sqrt 6)^2}{(\sqrt 3+\sqrt 6)(\sqrt 3-\sqrt 6)}\\\\\\=\dfrac{3-2\sqrt {18}+6}{3-6}\\\\\\=\dfrac{9-2\sqrt{18}}{-3}\\\\\\=-3+\dfrac{2}{3}\sqrt{18}.[/tex]
Thus, the answer is [tex]-3+\dfrac{2}{3}\sqrt{18}.[/tex]
