$$\frac{(\frac{5}{3}+\frac{1}{2})\cdot\frac{1}{5}-\frac{1}{10}}{\frac{3}{4}\cdot\frac{5}{7}-\frac{5}{6}+\frac{8}{15}}=$$
$\frac{140}{99}\approx 1.414141414$
$$\frac{\left(\frac{10}{6}+\frac{3}{6}\right)\times \frac{1}{5}-\frac{1}{10}}{\frac{3}{4}\times \frac{5}{7}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{10+3}{6}\times \frac{1}{5}-\frac{1}{10}}{\frac{3}{4}\times \frac{5}{7}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{13}{6}\times \frac{1}{5}-\frac{1}{10}}{\frac{3}{4}\times \frac{5}{7}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{13\times 1}{6\times 5}-\frac{1}{10}}{\frac{3}{4}\times \frac{5}{7}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{13}{30}-\frac{1}{10}}{\frac{3}{4}\times \frac{5}{7}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{13}{30}-\frac{3}{30}}{\frac{3}{4}\times \frac{5}{7}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{13-3}{30}}{\frac{3}{4}\times \frac{5}{7}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{10}{30}}{\frac{3}{4}\times \frac{5}{7}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{\frac{3}{4}\times \frac{5}{7}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{\frac{3\times 5}{4\times 7}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{\frac{15}{28}-\frac{5}{6}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{\frac{45}{84}-\frac{70}{84}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{\frac{45-70}{84}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{-\frac{25}{84}+\frac{8}{15}}$$
$$\frac{\frac{1}{3}}{-\frac{125}{420}+\frac{224}{420}}$$
$$\frac{\frac{1}{3}}{\frac{-125+224}{420}}$$
$$\frac{\frac{1}{3}}{\frac{99}{420}}$$
$$\frac{\frac{1}{3}}{\frac{33}{140}}$$
$$\frac{1}{3}\times \frac{140}{33}$$
$$\frac{1\times 140}{3\times 33}$$
$$\frac{140}{99}$$
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$\frac{2 ^ {2} \cdot 5 \cdot 7}{3 ^ {2} \cdot 11} = 1\frac{41}{99} = 1.4141414141414141$
