Factor $108=6^{2}\times 3$. Rewrite the square root of the product $\sqrt{6^{2}\times 3}$ as the product of square roots $\sqrt{6^{2}}\sqrt{3}$. Take the square root of $6^{2}$.
Factor $48=4^{2}\times 3$. Rewrite the square root of the product $\sqrt{4^{2}\times 3}$ as the product of square roots $\sqrt{4^{2}}\sqrt{3}$. Take the square root of $4^{2}$.
Fraction $\frac{-12}{5}$ can be rewritten as $-\frac{12}{5}$ by extracting the negative sign.
$$18\sqrt{3}-\frac{12}{5}\sqrt{3}-\sqrt{75}$$
Combine $18\sqrt{3}$ and $-\frac{12}{5}\sqrt{3}$ to get $\frac{78}{5}\sqrt{3}$.
$$\frac{78}{5}\sqrt{3}-\sqrt{75}$$
Factor $75=5^{2}\times 3$. Rewrite the square root of the product $\sqrt{5^{2}\times 3}$ as the product of square roots $\sqrt{5^{2}}\sqrt{3}$. Take the square root of $5^{2}$.
$$\frac{78}{5}\sqrt{3}-5\sqrt{3}$$
Combine $\frac{78}{5}\sqrt{3}$ and $-5\sqrt{3}$ to get $\frac{53}{5}\sqrt{3}$.
