how to simplify $\frac{2+\sqrt{3}}{6+4\sqrt{3}}$ among solving a problem I need to simplify: $$\frac{2+\sqrt{3}}{6+4\sqrt{3}}$$
I know it is $\frac{1}{2\sqrt{3}}$ but I dont know how to show that in mathematic way for example I can write $$\frac{2+\sqrt{3}}{2\sqrt{3}(\sqrt{3}+2)}$$ but still not obvious.Is there better way to prove/show that?

If in doubt, use conjugates:
$$ \frac{2+\sqrt 3}{6+4\sqrt 3}=\frac{2+\sqrt 3}{2\cdot (3+2\sqrt 3)}=\frac{(2+\sqrt 3)(3-2\sqrt 3)}{2\cdot (3+2\sqrt 3)(3-2\sqrt 3)}=\frac{-\sqrt 3}{-6}=\frac1{2\sqrt 3}$$
