[tex][1\frac{1}{12}-2\frac{2}{3}-(-2\frac{1}{2})]:(\frac{5}{6}+(-1\frac{3}{4})]=\\\\=(1\frac{1}{12}-2\frac{2}{3}+2\frac{1}{2}):(\frac{5}{6}-1\frac{3}{4})=\\\\=(1\frac{1}{12}-2\frac{8}{12}+2\frac{6}{12}):(\frac{5}{6}-\frac{7}{4})=\\\\=(\frac{13}{12}-\frac{32}{12}+\frac{30}{12}):(\frac{20}{24}-\frac{42}{24})=\frac{13-32+30}{12}:\frac{20-42}{24}=\\\\=\frac{11}{12}:(-\frac{22}{24})=\frac{11}{12}\cdot(-\frac{24}{22})=\boxed{-1}[/tex]
