[tex] \dfrac{x}{y} = \dfrac{1}{5} \Rightarrow y=5x \\ \\ \dfrac{z}{y} = \dfrac{2}{3} \Rightarrow z= \dfrac{2 \cdot y}{3} = \dfrac{2 \cdot 5x}{3} = \dfrac{10x}{3} \\ \\ \\ \dfrac{z+y}{x} = \dfrac{\dfrac{10x}{3}+5x}{x} = \dfrac{\dfrac{10x+15x}{3}}{x} = \dfrac{\dfrac{25x}{3}}{x} = \dfrac{25x}{3} \cdot \dfrac{1}{x} = \dfrac{25}{3} \\ \\ \\ \dfrac{a}{2} = \dfrac{3}{b} \Rightarrow a \cdot b= 6 \\ 6=6 \cdot 1 = 1 \cdot 6 = 2 \cdot 3 = 3 \cdot 2 = (-1) \cdot (-6) = (-6) \cdot (-1) = (-2) \cdot (-3) = (-3) \cdot (-2) \Rightarrow (a,b) = (1;6) ; (6,1) ; (2,3) ; (3,2) ; (-1, -6) ; (-6, -1); (-2, -3) ; (-3, -2) [/tex]
