\(\left(\frac{15\left(\sqrt{6}-2\right)\left(3-\sqrt{6}\right)+4\left(\sqrt{6}+1\right)\left(3-\sqrt{6}\right)-12\left(\sqrt{6}+1\right)\left(\sqrt{6}-2\right)}{\left(\sqrt{6}+1\right)\left(\sqrt{6}-2\right)\left(3-\sqrt{6}\right)}\right)=\left(\frac{15\left(3\sqrt{6}-6-6+2\sqrt{6}\right)+4\left(3\sqrt{6}-6+3-\sqrt{6}\right)-12\left(6-2\sqrt{6}+\sqrt{6}-2\right)}{\left(\sqrt{6}+1\right)\left(\sqrt{6}-2\right)\left(3-\sqrt{6}\right)}\right)=(\frac{\left(15\left(5\sqrt{6}-12\right)+4\left(2\sqrt{6}-3\right)-12\left(4-\sqrt{6}\right)\right)}{18-7\sqrt{6}})=\left(\frac{75\sqrt{6}-180+8\sqrt{6}-12-48+12\sqrt{6}}{18-7\sqrt{6}}\right)=\left(\frac{95\sqrt{6}-240}{18-7\sqrt{6}}\right)=\left(\frac{95\sqrt{6}-240}{7\sqrt{6}-18}\right)\)