$$\frac{(\frac{5}{3}+\frac{1}{2})\cdot\frac{1}{5}-\frac{1}{10}}{\frac{3}{4}\cdot\frac{5}{6}+\frac{8}{15}}=$$
$\frac{40}{139}\approx 0.287769784$
$$\frac{\left(\frac{10}{6}+\frac{3}{6}\right)\times \frac{1}{5}-\frac{1}{10}}{\frac{3}{4}\times \frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{10+3}{6}\times \frac{1}{5}-\frac{1}{10}}{\frac{3}{4}\times \frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{13}{6}\times \frac{1}{5}-\frac{1}{10}}{\frac{3}{4}\times \frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{13\times 1}{6\times 5}-\frac{1}{10}}{\frac{3}{4}\times \frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{13}{30}-\frac{1}{10}}{\frac{3}{4}\times \frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{13}{30}-\frac{3}{30}}{\frac{3}{4}\times \frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{13-3}{30}}{\frac{3}{4}\times \frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{10}{30}}{\frac{3}{4}\times \frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{\frac{3}{4}\times \frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{\frac{3\times 5}{4\times 6}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{\frac{15}{24}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{\frac{5}{8}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{\frac{75}{120}+\frac{64}{120}}$$
$$\frac{\frac{1}{3}}{\frac{75+64}{120}}$$
$$\frac{\frac{1}{3}}{\frac{139}{120}}$$
$$\frac{1}{3}\times \frac{120}{139}$$
$$\frac{1\times 120}{3\times 139}$$
$$\frac{120}{417}$$
$$\frac{40}{139}$$
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$\frac{2 ^ {3} \cdot 5}{139} = 0.28776978417266186$
