Question

(1/5+1/3):(3/5-1/15)+0,9999

Answer 1

$\ \ \ (\frac{1}{5} + \frac{1}{3}):( \frac{3}{5}- \frac{1}{15})+0,999...\\ \\=(\frac{5}{15} + \frac{3}{15}):( \frac{9}{15}- \frac{1}{15})+1\\ \\=(\frac{5+3}{15}):( \frac{9-1}{15})+1\\ \\=(\frac{8}{15}):( \frac{8}{15})+1\\ \\=(\frac{8}{15}) \cdot( \frac{15}{8})+1\\ \\=(\frac{120}{120})+1\\ \\=1+1\\ =2$

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$\ \ \ (\frac{1}{5} + \frac{1}{3}):( \frac{3}{5}- \frac{1}{15})+0,9999\\ \\=(\frac{5}{15} + \frac{3}{15}):( \frac{9}{15}- \frac{1}{15})+0,9999\\ \\=(\frac{5+3}{15}):( \frac{9-1}{15})+0,9999\\ \\=(\frac{8}{15}):( \frac{8}{15})+0,9999\\ \\=(\frac{8}{15}) \cdot( \frac{15}{8})+0,9999\\ \\=(\frac{120}{120})+0,9999\\ \\=1+0,9999\\ \\ =1,9999$