$~~~\frac{\sqrt{12}-3}{5\sqrt{3}-10}$
$=\frac{(\sqrt{12}-3)(5\sqrt{3}-10)}{(5\sqrt{3}-10)(5\sqrt{3}-10)}$
$=\frac{10(\sqrt{3})^2+20\sqrt{3}-15\sqrt{3}-30}{(5\sqrt{3})^2-10^2}$
$=\frac{30-5\sqrt{3}-30}{25.3-100}$
$=\frac{5\sqrt{3}}{-25}$
$=-\frac{\sqrt{3}}{5}$
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