$$( 3 \frac { 1 } { 4 } - 2 \frac { 3 } { 5 } ) \div ( 5 \frac { 2 } { 3 } + 1 \frac { 1 } { 2 } )=$$
$\frac{39}{430}\approx 0.090697674$
$$\frac{\frac{12+1}{4}-\frac{2\times 5+3}{5}}{\frac{5\times 3+2}{3}+\frac{1\times 2+1}{2}}$$
$$\frac{\frac{13}{4}-\frac{2\times 5+3}{5}}{\frac{5\times 3+2}{3}+\frac{1\times 2+1}{2}}$$
$$\frac{\frac{13}{4}-\frac{10+3}{5}}{\frac{5\times 3+2}{3}+\frac{1\times 2+1}{2}}$$
$$\frac{\frac{13}{4}-\frac{13}{5}}{\frac{5\times 3+2}{3}+\frac{1\times 2+1}{2}}$$
$$\frac{\frac{65}{20}-\frac{52}{20}}{\frac{5\times 3+2}{3}+\frac{1\times 2+1}{2}}$$
$$\frac{\frac{65-52}{20}}{\frac{5\times 3+2}{3}+\frac{1\times 2+1}{2}}$$
$$\frac{\frac{13}{20}}{\frac{5\times 3+2}{3}+\frac{1\times 2+1}{2}}$$
$$\frac{\frac{13}{20}}{\frac{15+2}{3}+\frac{1\times 2+1}{2}}$$
$$\frac{\frac{13}{20}}{\frac{17}{3}+\frac{1\times 2+1}{2}}$$
$$\frac{\frac{13}{20}}{\frac{17}{3}+\frac{2+1}{2}}$$
$$\frac{\frac{13}{20}}{\frac{17}{3}+\frac{3}{2}}$$
$$\frac{\frac{13}{20}}{\frac{34}{6}+\frac{9}{6}}$$
$$\frac{\frac{13}{20}}{\frac{34+9}{6}}$$
$$\frac{\frac{13}{20}}{\frac{43}{6}}$$
$$\frac{13}{20}\times \frac{6}{43}$$
$$\frac{13\times 6}{20\times 43}$$
$$\frac{78}{860}$$
$$\frac{39}{430}$$
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$\frac{3 \cdot 13}{2 \cdot 5 \cdot 43} = 0.09069767441860466$
