{ m, n, p } d.p. { 1, 5, 7 } [tex] \Longrightarrow \dfrac{m}{1} = \dfrac{n}{5} = \dfrac{p}{7} = k [/tex], unde k = coeficient de proporționalitate
Și avem : m = k, n = 5k, p = 7k
[tex]a) \: \dfrac{m + n + p}{p + n - m} = \dfrac{k + 5k + 7k}{7k + 5k - k} = \dfrac{13k}{11k} = \boldsymbol {\dfrac{13}{11} } \\ [/tex]
[tex]b) \: \dfrac{3m + 2n + p}{2m + 4n + p} = \dfrac{3k + 2 \cdot5k + 7k}{2k + 4 \cdot5k + 7k} = \dfrac{3k + 10k + 7k}{2k + 20k + 7k} = \\ [/tex]
[tex] = \dfrac{20k}{29k} = \boldsymbol {\dfrac{20}{29}} [/tex]
[tex]c) \dfrac{10m - n + 2p}{m + p} = \dfrac{10k - 5k + 2 \cdot7k}{k + 7k} = \dfrac{5k + 14k}{8k} = \\ [/tex]
[tex] =\dfrac{19k}{8k} = \boldsymbol {\dfrac{19}{8}} \\ [/tex]
