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JoshSK
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[tex]\displaystyle \frac{ \frac{1}{2} +3: \frac{5}{4} }{14 \cdot \frac{3}{5} -1: \frac{5}{13} } = \frac{ \frac{1}{2} +3 \cdot \frac{4}{5} }{ \frac{42}{5} -1 \cdot \frac{13}{5} } = \frac{ \frac{1}{2} + \frac{12}{5} }{ \frac{42}{5} - \frac{13}{5} } = \frac{ \frac{5}{10} + \frac{24}{10} }{ \frac{29}{5} } = \frac{ \frac{29}{10} }{ \frac{29}{5} } = \\ \\ \\ = \frac{29}{10} : \frac{29}{5} = \frac{29}{10} \cdot \frac{5}{29} = \frac{145}{290} = \frac{1}{2} [/tex]