$$9 \frac { 3 } { 4 } \div [ 2 \frac { 1 } { 6 } + \{ 4 \frac { 1 } { 3 } - ( 1 \frac { 1 } { 2 } + 1 \frac { 3 } { 4 } ) \} ]$$
$3$
$$\frac{\frac{36+3}{4}}{\frac{2\times 6+1}{6}+\frac{4\times 3+1}{3}-\left(\frac{1\times 2+1}{2}+\frac{1\times 4+3}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{2\times 6+1}{6}+\frac{4\times 3+1}{3}-\left(\frac{1\times 2+1}{2}+\frac{1\times 4+3}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{12+1}{6}+\frac{4\times 3+1}{3}-\left(\frac{1\times 2+1}{2}+\frac{1\times 4+3}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{4\times 3+1}{3}-\left(\frac{1\times 2+1}{2}+\frac{1\times 4+3}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{12+1}{3}-\left(\frac{1\times 2+1}{2}+\frac{1\times 4+3}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{13}{3}-\left(\frac{1\times 2+1}{2}+\frac{1\times 4+3}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{13}{3}-\left(\frac{2+1}{2}+\frac{1\times 4+3}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{13}{3}-\left(\frac{3}{2}+\frac{1\times 4+3}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{13}{3}-\left(\frac{3}{2}+\frac{4+3}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{13}{3}-\left(\frac{3}{2}+\frac{7}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{13}{3}-\left(\frac{6}{4}+\frac{7}{4}\right)}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{13}{3}-\frac{6+7}{4}}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{13}{3}-\frac{13}{4}}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{52}{12}-\frac{39}{12}}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{52-39}{12}}$$
$$\frac{\frac{39}{4}}{\frac{13}{6}+\frac{13}{12}}$$
$$\frac{\frac{39}{4}}{\frac{26}{12}+\frac{13}{12}}$$
$$\frac{\frac{39}{4}}{\frac{26+13}{12}}$$
$$\frac{\frac{39}{4}}{\frac{39}{12}}$$
$$\frac{\frac{39}{4}}{\frac{13}{4}}$$
$$\frac{39}{4}\times \frac{4}{13}$$
$$\frac{39\times 4}{4\times 13}$$
$$\frac{39}{13}$$
$$3$$
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