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Rearrange suitably and find the sum in each case 3/4+ -2/5+ -5/-12+ 2/3+ 5/-6? the answer in my book is ⅗. please explain it please ​

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ANSWER:

we \: can \: rearrange \: it \: in \: this \: way \\ \\ = \frac{3}{4} + \frac{ - 2}{5} + \frac{2}{3} + \frac{ - 5 }{ - 12} + \frac{5}{ - 6} \\ \\ we \: can \: add \: \frac{ - 5 }{ - 12} + \frac{5}{ - 6} \: separately \: \\ \\ and \:\frac{ 2}{5} + \frac{2}{3} \: separately \\ \\ \frac{ - 5 }{ - 12} + \frac{5}{ - 6} = \frac{ - 6 \times - 5 + 5 \times - 12}{ - 6 \times - 12} = \frac{30 + - 60}{72} = \frac{ - 30}{72} \\ \\ \frac{ - 30}{72} = \frac{ - 15}{36} = \frac{ - 5}{12} \\ \\ \frac{ - 2}{5} + \frac{2}{3} = \frac{3 \times - 2 + 2 \times 5}{15} = \frac{ - 6 + 10}{15} = \frac{4}{15} \\ \\ now \: \frac{4}{15} + \frac{ - 5}{12} + \frac{3}{4} \\ \\ \frac{ - 5}{12} + \frac{3}{4} = \frac{ - 5 \times 4 + 3 \times 12}{12 \times 4} = \frac{ - 20 + 36}{48} = \frac{16}{48} \\ \\ \frac{16}{48} = \frac{8}{24} = \frac{1}{4} \\ \\ \frac{1}{4} + \frac{4}{15} = \frac{15 + 16}{60} = \frac{31}{60}

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